OPTIFINE: Optifine is a "mod" that allows even more options customization-wise. Just downloading it alone boosts FPS, but you can take it a step further in your settings. I would go into detail, but it would be too long to give you all the details. Optifine can be found here: https://optifine.net/home
V-SYNC: First, what is V-Sync? V-sync is the best limit of FPS that your monitor can handle. Even if you set the FPS limit in game to infinite, your monitors V-Sync will still override the limit you set. If you turn it off, you will see FPS improvement (WARNING: There may also be some screen tears. YOU HAVE BEEN WARNED). The V-Sync option is found in Options<Video Settings. It will be on the right side.
UPDATING: It is crucial you keep your Java version up-to-date as well as your graphics cards. What? You didn't know you can update your graphics card? Well, you can! As long as your card manufacturer provides updates for them (NOTE: These "updates" are SOFTWARE updates, meaning over the web. Be careful from who you download and make sure it is the manufacturer!).
PRIORITIZING: It is wise to shut down all programs in order for your desired program to work. The more programs open, then more RAM used, the harder you make your computer work, which is bad.
WARNING: It is DANGEROUS for you to set your RAM usage to anything ABOVE half of your total RAM! It can damage your RAM and lower your RAMs total amount!