how to improve macbook pro mid 2009

For the slow performance, you can usually do a clean install of OS X and sometimes that will remedy slow speed on older macbooks.

As for the low battery life, If you are the "on the go" kind of person, then that could be a problem. If you are NOT an "on the go" kind of person, you can keep it plugged in all the time.

If it still has the original battery, that needs to be replaced. Also you would need to add memory. 2 GB is not enough for full performance in Mavericks.

That model has a max possible RAM fo 8GB (two 4GB modules). As long as you are not doing anything heavy-duty, 4GB (two 2GB modules) is probably OK for Mavericks. I have on MBP running Mav on 4GB with no indications it is struggling for more RAM.

Only buy RAM from a trusted Mac RAM reseller. I use Other World Computing (their RAM listings for your model are here):

http://eshop.macsales.com/shop/memory/Apple_MacBook_MacBook_Pro/Upgrade/DDR3

Crucial.com is also good. Avoid Kingston ValuRAM. It has never been happy in Intel Macs. You will get the right RAM from either vendor. Can't say that for brick-n-mortar electronics stores. Too hard to find one with a resident geek who speaks Mac.

Installation is an easy do-it-yourself task; all you need is the right screwdriver. Handy video here:

http://eshop.macsales.com/installvideos/macbookpro_13_unibody/

As for the battery, there is a built-in utility that will show the current condition. Click and hold on your Apple menu. Hold down the OPTION key and the first item with change to System Information. Launch it. When it comes up. find "Power" in the left-hand contents pane and select it to get a battery report. Looks like this:

Copy the information I've outlined in red and paste it into a response to your thread here. Those numbers describe the current condition of the battery.