Hello and welcome traveller.
I have been asked many a question on how to set up various emulators, so I decided to create this thread you see before you.
For this is my new undertaking to explain the ins and outs of emulator set up.

A few key terms for you;
ROM, ISO, 'Image': The name used for a game that you play on an emulator.
ROM for cartridge based games like NES, and ISO or 'Image' for CD/DVD based games like Playstation.
Emulator: The program that you use on your computer to play games from different systems.
Archive: A file thats used to store other files together inside it, like a folder.
Split Archive: An archive that has been broken into parts for various reasons, often to make it easier to download or transfer.
Sometimes contains another full archive inside it which will also need extracting.
Extract: The method you use to take the files out of the archive so you can use them.
Click: Yes I know its a simple enough term, but sometimes it can be confusing to some.
When I say click I mean click with the left mouse button. I'll say to click with the right mouse button if you need to do so.
BIOS: CD/DVD based game consoles need a special file, called BIOS, to run properly.
They normally go in a special folder in the emulator folder.

A few useful programs for you;
WinRAR: This is an archive program, used to make and extract archives.
It has paid and trial versions, the trial lasts 40 days at last check.
Worth mentioning because it is very useful, works very well.
Link: http://www.rarsoft.com/
7-Zip: Another archive program, used to make and extract archives.
I prefer WinRAR, but 7-Zip is free to use so it might be a better alternative for you.
Link: http://www.7-zip.org/

Alcohol 120%: A program you can use to make ISOs of CD/DVD games and burn ISOs for use on a console.
It has paid and trial versions, the trial lasts 15 days at last check.
Worth mentioning because it is very useful, works very well.
Link: http://www.alcohol-soft.com/
ImgBurn: A program you can use to make ISOs of CD/DVD games and burn ISOs for use on a console.
Its free, so it may be more useful to you then Alcohol 120%, but I havn't used it so I can't say how reliable it is.
Link: http://www.imgburn.com/

I will be trying to create as easy an experience for you all as I can, so I have tried to explain things in the best way possible.
These guides are laid out in a step by step fashion, as I set up and used each emulator.
Now with that in mind, let the thread commence!

(Though for now it will remain closed as I add guides to it In the mean time, feel free to PM me if you need any help)

EDIT: added info about BIOS, Clicking and a PM link

nullDC 'Dreamcast' emulator setup guide

This sets up nullDC for USA NTSC region games.
These are the files needed for nullDC.
nullDC 1.0.3: http://www.filesend.net/download.php?f=a25cdee365fc462d9deb58b7d45b3bc8
nullDC BIOS: http://www.filesend.net/download.php?f=0d98fd6bf0bb877c46a3a4fa80435a4a
d3dx9_37.dll: http://www.filesend.net/download.php?f=bc667119c9a7d027ea3990b5fb476bd2
Game of your choice: http://www.get-your-rom.com/DREAMCAST.php

Download the above mentioned files to your computer.
Extract the nullDC_103 archive to a folder of your choice.
Extract the nullDC_bios archive to the 'data' folder in your nullDC folder.
Extract the d3dx9_37 archive to your nullDC folder.
Extract the game archive to a folder of your choice.
(ProTip - Get to know your folders, name them so that you know whats in them.
Example: I name my emulator folders after the emulator, so in this case, the folder would be 'nullDC')

In the nullDC folder there is a file called nullDC_1.0.3_mmu.
Run the nullDC_1.0.3_mmu file to start the emulator.
This is often easiest to do by clicking the file with the left mouse button then pressing the 'Enter' key on your keyboard.

To configure the controls, click Options, then Maple, Port A and finally Config keys for Player 1.
Click a button on the box that appears then press the keyboard key,
or controller button if you have one plugged in, you want to use for the button named.
When you are done click OK.

To start the emulator in Dreamcast console mode, click File, Normal Boot then click No Disk.
You can use console mode to set up options like date and time for the console as well as manage save games.

To start the emulator in game mode, click File, Normal Boot, click the three dots "..." to bring up the game browser,
browse to the folder you have the game in, click on the game then click Open.

If you start the emulator in either game or console mode and you want to swap disks in game mode,
start a new game from console mode or swap from game mode to console mode,
you have to click Options, GDRom, Swap Disk then either use the three dots "..." and Open to select the new disk,
or click No Disk to return to the console.
If you chose to select a new disk you will need to select Play in the console to start the disk.

ePSXe 'Playstation' emulator setup guide
You can view the video tutorial of this process by Rasenganfan2 on YouTube at http://www.youtube.com/watch?v=yjk17BE0dd4

This sets up ePSXe for USA NTSC region games.
These are the files needed for ePSXe.
ePSXe 1.7.0: http://www.filesend.net/download.php?f=f49f700668c4f570c57614fbeb2c8b11
ePSXe BIOS: http://www.filesend.net/download.php?f=1f3da46aed9af67f317ca4e994f7fbd5
Pete's GPU plugin pack 1.77: http://www.filesend.net/download.php?f=64079074e8b699ee685d33cc55020a2b
zlib1.dll: http://www.filesend.net/download.php?f=58bf77054b658f977c0baaa62c80377d
Game of your choice: http://www.get-your-rom.com/PLAYSTATION.php

Download the above mentioned files to your computer.
Extract the epsxe170 archive to a folder of your choice.
Extract the ePSXe_bios archive to the 'bios' folder in your ePSXe folder.
Extract the gpupete177 archive to the 'plugins' folder in your ePSXe folder.
Extract the zlib1 archive to your ePSXe folder.
Extract the game archive to a folder of your choice.

If you plan to use a USB or other type of controller, plug it in and set it up now.

In the ePSXe folder there is a file called ePSXe.
Run the ePSXe file to start the emulator.
Do this by clicking the file then pressing the 'Enter' key on your keyboard.

A 'Wizard' should pop up to help you configure ePSXe, if it doesn't click Config then Wizard Guide.
Read the message if you want then click the button which says Config >>
Click on 'scph1001 - USA (Recommended)' from the list shown to highlight it and click the button which says Next >>
Click on 'Pete's DX6 D3D Driver 1.77' from the list shown to highlight it and click the button which says Next >>
Leave 'ePSXe SPU core 1.7.0.' highlighted (or click it if its not) and click the button which says Next >>
Leave whichever option is highlighted as it is and click the button which says Next >>

Click the button which says 'Controller 1' to configure the first controller.
From the drop down list in the top right corner select '[SCPH-1080] Digital'
or select '[SCPH-1150] DualAnalog' if you want to use an analog controller.
Click a box in the window then press the keyboard key, or controller button if you have one plugged in,
that you want to use for the button the line from the box leads to.
When you are done click OK. Repeat these steps if you want to set up 'Controller 2'.
When you are done with configuring the controllers, click the button which says Next >>
Read the message if you want then click the button which says Done.

To start the emulator in Playstation console mode, click File then Run BIOS.
You can use console mode to manage save games.

To start the emulator in game mode, click File then Run ISO to bring up the game browser,
browse to the folder you have the game in, click on the game then click Open.
Keep in mind that some games will show up 2 or more times in the browser,
but they both start the same game so it doesn't matter which one you choose.

If you start the emulator in game mode and you have to swap disks, for example with a multi disk game.
When prompted to change disks by the game, press the 'Esc' (or escape) key on your keyboard
to bring back the main emulator screen, click File, Change Disk, then ISO to bring up the game browser,
browse to the folder you have the game in, click on the game then click Open.

Nestopia 'NES' emulator setup guide

This sets up Nestopia for all region games.
These are the files needed for Nestopia.
Nestopia 1.4: http://www.get-your-rom.com/emulators.php
Game of your choice: http://www.get-your-rom.com/nesroms.php

Download the above mentioned files to your computer.
Extract the Nestopia140bin archive to a folder of your choice.
Extract the game archive to a folder of your choice.

If you plan to use a USB or other type of controller, plug it in now.

In the Nestopia folder there is a file called nestopia.
Run the nestopia file to start the emulator.
Do this by clicking the file then pressing the 'Enter' key on your keyboard.

To configure the controls, click Options, then Input.
To set controls for player 1, click Pad 1 in the Type column then click the word in the
Mapping column thats next to the the button you want to set up in the Key column.
Click the Set button at the bottom of the Mapping column then press the keyboard key,
or controller button if you have one plugged in, you want to use for the button named.
Repeat this process for each button you wish to set up.
To set controls for player 2, click Pad 2 in the Type column and repeat the process above.
When you are done click OK.

To start a game, click File then Open to bring up the game browser,
browse to the folder you have the game in, click on the game then click Open.

To change the size of the game window, click View, then Screen Size,
then choose if you want to have the game window at 2 times its size,
3 times its size, or using the whole screen.
I do not recomend using the whole screen as on some screens it will look strange.

To use the Save State feature (a way to save games with no save function),
press the F5 key on your keyboard then name the save file, or leave the name as it is,
and press the Save button.
To load the saved game, start the game you want to load the save for,
press the F7 key on your keyboard, choose the save name from the browser and click Open.