Just because you have Yosemite doesn't mean you have a "newer" MBP.
I have a 2010 and it will run Yosemite as well.. according to this list your MBP could be as old as 2007
Here's a List of Macs Compatible With OS X Yosemite
Go to About this Mac under the apple in the top left of you desktop..
>More Info..
>System report in the overview tab
Then in that window 2nd line from the top youll see something that says MacBook Pro x, y. That lets us know how old it is and if-so-facto how much RAM the MBP can take.
As for properly closing Apps/programs.. as your reading this go to the top left of your window and click the Safari (or what ever web browser you use) drop down.. at the very bottom it will say 'Quit _____". If you hit that you are properly closing the application. The fast way is to hit Command+Q (that is the same as Alt+F4 if you are familiar with windows). Command+Q works with every application that I use on a regular basis.. exclude maybe some games idk about. You need to close things properly or you will get memory sucked into these background apps all the time. Your mac isn't like an iPhone/iPad/iPod since they do not get bogged down with 15 games open in the background.
Once you start closing apps correctly.. check and see what apps you have opening at boot up..
>System Preferences
>Users and Groups
>Login Items
If there is a lot of things on that list (that are check marked) take some things off.. that will help if rebooting doesn't work.
Once you've done those things.. and After clearing caches, checking permissions, making sure the HD isnt more than 85% full (you never told us how big your HD is), checking how many apps you have open (hitting Command+Tab will show you the major ones that would use the most resources), & rebooting your computer... I would recommend getting more ram if your problem persists.
Go to everymac.com to see the max capacity ram for your model (Macbook x,y). APple will often only offer to sell you a certain amount of ram when the machine will in fact utilize more.. that is not always the case but some times it is.
From what you said above-your MBP has 2 2GB Ram sticks installed. That means if you get the biggest pair of Ram sticks it could possibly (DEPENDING ON YOUR MODEL)go to 16GB (2x8GB), you may not be able to go that high.. but almost certainly could go to 8 GB (2x4GB sticks. You'll figure that out once you find your model under everymac.com.
hth