I have noticed that a huge amount of my phones RAM usage has gone up since I received the new update. Performance seems to be fine, but out of 1.5 gigs of RAM, it is using 1.3 or so all the time. Is this normal?
Yes, that is completely normal. Android loads apps into RAM that it thinks you will be using. This is for faster load times and is a multitasking feature. If a different app tries to load and more RAM is needed, an app will be kicked out as needed.
It's cached not running. Like Demmo says the cache gets dumped when you need more ram. Cached apps do not use your battery. Ram is ram and it uses the same power whether it is empty or not. Processes is what you need to look for when you are worried about battery life.
Good rule of thumb use the back button(caches the app) when exiting apps and never the home button(allows the app to run in the background and use processes). This
I was wondering if hitting the back button is enough or if you also have to close them from the task manager. I saw a video where they closed the apps by long pressing the home button and hitting "remove all". That seems to be a bit much.
That would remove all the cached apps.
Going into task manager and clearing ram will stop all running and wipe cache. As soon as you get out of it things start to load like your launcher, widgets, and some apps android knows it should keep as cached (your most used apps for example).