To begin if your phone is lagging when playing youtube it most likely has to do with your 3G/4G data signal as a poor signal can make the phone load at a slower pace. The first step to improve your signal would be to just do a quick reboot by holding down the power button, turning it off/and back on. If you don't see an improvement in your signal right away you may want to connect with your carrier to see if there is any provisioning that can be done on their in (or to see if a tower is being worked on). Another way to improve your internet/youtube speed would be to just connect to a wifi signal. Most people prefer to connect to wifi when streaming movies, and if you don't have unlimited data it saves you on using up your data.
Regarding your phone just overall not navigating well, you may have too many applications running in the background, so you may want to hold down your home button and close out some of the running apps. This can also be done by going to Menu>Settings>Manage apps>running> and force close
You should see improvement after these steps. If the issue continues you will want to backup your information and go ahead and do a factory reset. It's the ultimate troubleshooting step, but if there's something glitching in the software it needs to be done. Hope this helps!