As a Minecraft player, and server owner who has no money, I have had to deal with these issues many times; along with countless operating system re-installs, cloud management, Linux networking, you get to learn a few things. With my 5+year old 1.8 ghz duel core laptop with meager integrated graphics I can get upwards of 50 FPS.



1. Optifine. Even if you have a decent computer it will improve the frame rate. Optifine makes adjustments to the poorly written Minecraft display code, offering smoother FPS all around. Turning off all of the animations and extra visual elements is the best way to performance.
http://www.minecraftforum.net/topic/249637-125-optifine-hd-a6-fps-boost-hd-textures-aa-af-and-more/

2. Sun Java 9.0.1 Oracle Sun Java is more efficient than OpenJDK for running Minecraft.
http://www.oracle.com/technetwork/java/javase/downloads/index.html

3. LWJGL. Even if you don't fully understand what this does. Update your Minecraft bin with the new version. Do it. Trust me. Think of it as Unreal Engine or Frostbite 2.0 or something. Here is a tutorial on installation. (drag and drop)
http://www.minecraftwiki.net/wiki/Tutorials/Update_LWJGL

LWJGL is no longer required for the latest version of Minecraft.

4.Different Browser Sizes. You can either leave MC in it's original size or make it even smaller, which improves FPS significantly. Or turn down the screen resolution to its lowest setting in Optifine and play in fullscreen.

5. Tiny Render Distance/Smooth Lighting Off. If you have not done this yet, what are you waiting for! This is one of the best things you can do for FPS. Render distance is a killer and you will see a massive spike in FPS when it is lowered. Smooth Lighting also has an effect on performance. Turning performance to MAX FPS also helps a lot as well.

6. Higher Java Priority. In Windows, go into the Task Manager and enter the tab Processes. Find javaw.exe and right click it. Then select Set Priority and make it High. On Ubuntu open up the System Moniter and navigate to Processes as well. Find java and click Priority. A slider should appear and make sure it is set at -20 (High).

7.Get a Texture Pack with Few Colours. Even if it is a 64 bit texture pack, the amount of different colours is the only thing that matters (Not that you should get a 64 bit texture pack.) I would suggest SimpleCraft.
http://www.minecraftforum.net/topic/98584-16x125-simplecraft-for-full-classic-v104/

8. Update your Graphic Card's drivers. While I do not have a graphic card to update, pretty much most newer computers have a dedicated card. Look up your card and get the latest drivers. This will help massively.

9. Defrag your HDD. This will likely not only improve Minecraft performance but overall computer performance. Look up how to defragmentate (defrag) your hard drive for your OS and proceed. Make sure you defrag the drive that actually has MC saved on it.

10. Adjust your GPU for Minecraft. Nvidia cards will usually have a control panel. Navigate to your card's control panel an adjust the 3D performance settings for minecraft.exe for maximum performance.

11. Play on the downloaded client. Using the downloadable client is one of the easiest ways to improve Minecraft FPS.

12. Get a new GPU. See if your motherboard supports a GPU. If it does there are plenty of deals where you can get a decent budget GPU at reasonable cost. Check out reddit.com/r/buildapcsales for the latest deals.

13. Close all other applications. Minecraft is a system hog, let it have some room. Close all your other stuff down and enjoy some simple MC.

Good luck guys. Having low FPS really does suck. I hope this article helps :)