This whole thing. I try to download the game by going to this page:
Download
When you have bought the game, you can download the stand-alone launcher for Minecraft here. It will automatically update the game files with the latest version. You'll be able to play the game without an Internet connection if you've been online at least once.
Minecraft for Windows
Download Minecraft.exe. If given the option, save the file instead of running it. Save the file anywhere you'd like, then double-click the program to run.
Show all platforms
The Minecraft launcher was updated 01 July 2013. To get latest version of the game, make sure that you have downloaded the latest version of the launcher from the link above.
Multiplayer Server
If you're running on Windows and just want to set up a server easily, download minecraft_server.1.7.9.exe and run it.
If you want to run the server on any other OS or without GUI it's a bit more involved (see this wiki article for a tutorial). First make sure you can use java from the command line. On Linux and Mac OS X this should already be set up but on Windows you might have to tinker with the PATH environment variable. Download and run minecraft_server.1.7.9.jar with java -Xmx1024M -Xms1024M -jar minecraft_server.jar nogui.

After this I download the game to a Download Minecraft.exe, and I get this weird screen with a bunch of Java stuff on it. Then I download the online and I get the same kind of thing. What do I do?

That screen is supposed to happen. It happens with everyone who runs the official launcher, without exception, so that's not the problem. However, that screen is supposed to only last a few seconds before launching a screen that lets you sign-in and play.

So how long have you been waiting at the Java screen? Only a few seconds? If so, try waiting longer.

I might be having the same issue.
I think when he tries to play online, the Mojang symbol pops up and then it loops back to the login page (where you see all the updates and links and the giant PLAY button)
The only way I can get it to stop looping is if I make Minecraft run 1.7.2 or earlier, but once I revert back to 1.7.2 I can't go on VizzedVille because the server requires 1.7.8

There's the issue that I'm having, and I'm willing to bet his is the same

Cooliogb : Actually the two problems look completely different from what I read. He doesn't even see the screen with the 'play' button.

I looked into your problem a little. I'm not entirely certain what the cause is, but this is what I found: 
1) It might be caused by an excess of mods (having too many mods causes the game to crash and loop like how you described)
2) Try re-downloading the launcher.

So single-player works fine, it's just online that has the loop?

I hope that helps.

In my defense, I totally don't understand anything XD
I've never tried playing offline, that option only comes up when my internet connection is down. Do I have to manually turn off internet or is there an option for that?
I'll uninstall it completely and try again.

EideticMemory : I waited about 5 minutes and nothing happened. The screen was still just there. I can play offline, but when I try to play online nothing happens. When I hit the login button, it says I can not connect to the minecraft.net server.
EideticMemory :

Barathemos : Sorry about the delay. Hmmm, okay. If you can play offline then it might be a firewall error.

Try-
1) Firewall Error Solution

Check out-
2) If you're getting: Internal Client error: session.minecraft.net

Cooliogb : Yes. As far as I know, you need to disconnect your internet to 'play offline'.

So any updates? How did the re-install go?

Its a hardware issue; I need a new graphics card for OpenGL 2.1
Thanks anyway.

Cooliogb : I'm glad that you found what's wrong. That was one abnormal problem. Hopefully you have another device to play it on for the time being? =/

Anyway, no problem. It's my job. I try to help out when I see questions unanswered.

I have a class in a computer lab at school at the start of each day, so I go on there and play it (sometimes against my teacher's will, which doesn't help cause he has hawk eyes and can detect when I'm goofing off like some sort of sixth sense).