Is there anyway to improve RAM on a Acer Extensa 5260?

Alrighty, steps, here you go.

It appears that computer comes with 2GB of RAM. It also appears to be running Windows Vista. So true step one is to install Windows 8.1. That alone will put you at twice as fast a computer you had before and do more than any RAM upgrade will do. It's a night-and-day difference, for me on my desktop, from Windows 7 to Windows 8.1. If this is not enough or is something you don't want to do…
Step one, open up your computer. See if the RAM sticks installed are either 2 1GB stick of memory OR 1 single stick of 2GB memory.
2. Does this amount of memory fill up all slots for RAM? If you have one stick and one free slot open, buying another 2 GB stick that runs at the same speed and has the same latency. I have already searched, however and can't find these stats. If you know how to open up your computer and take the RAM out (pretty simple), give us a picture of the RAM and all of the numbers and "stuff" on it.
3. If you have ONE slot available to you on that computer, buy a SINGLE 4 GB stick of RAM. This will probably exceed your budget by $10 or less, depending on the speed of it. If you have TWO slots in the computer for memory, then buy the SAME 4 GB memory stick module, BUT you can KEEP the old one in place too, so now you have 6GB of RAM which is plenty!

EDIT: I found this out what you need. You won't be getting 6GB memory total, but 4 will do http://www.amazon.com/...000PMGZDO/

USED options seem to be roughly in your budget.

If you operating system is 32-bit then 4 GB is all it will handle. If your operating is 64-bit then you can most likely go to 8 GB.

Win8 will NOT double your PC speed. Something was wrong with a computer that doubles performance from Win 7 to Win 8, and installing the new OS fixed the issue by eliminating it from the PC. Re-installing Win 7 would have done the same thing.