I have compiled some of ways to fix lag on crap computers. I am on a gaming pc with an ATI Radeon 6870 my self, and I still use OptiFine of these because it increases graphics and adds HD texture support too!

BOTH OF THESE METHODS ARE EASIEST ON WINDOWS, BUT FOR OPTIFINE THERE IS A WAY POSTED ON THE FORUM THREAD, AND I AM NOT SURE HOW TO DO A RAMDISK ON MAC (I DO SOMEWHAT ON LINUX)

METHOD 1
1. Force update your game (options, force update, then log in)
2. Close Minecraft
3. Download OptiFine (I recommend the HD_S_A): http://www.minecraftforum.net/topic/249637-181-optifine-hd-a-fps-boost-hd-textures/
4. Install OptiFine and delete META-INF (google how to install a minecraft mod)
5. Play minecraft!

METHOD 2 (harder and less effective than method 1)
http://www.youtube.com/watch?v=Wh7ZyFdHT48

METHOD 3 (CANT be used with the other methods and not as good as them, but is easy on mac)
http://dev.bukkit.org/client-mods/spoutcraft/

Using both methods at once will make it WAY less laggy.

I will update this blog as new methods are found. Comment telling me your method!