Disable mipmaps. (Warning: this can result in water/lava drips not being visible and taking a lava bath.)
Disable biome smoothing.
Set the game to small screen mode, as this makes the game load less on screen, making the game run a little bit faster. However for computers which have a better graphics card, change your settings, so Minecraft is in full screen mode, this makes the GPU focus more on Minecraft and less on other programs. Test both ideas and see which setting works best!
Also note, close any programs in the background and close any internet browsers.