With 512MB of RAM, unless you're using all of it through your Windows OS an upgrade isn't needed. The benefits of having 1GB allows you to play more memory hogging games, do some more intensive photo editing, video editing, etc etc. So with the current memory you have for the things you do on your computer, an upgrade isn't really needed.
To check if you need it:
For Windows XP or earlier:
-Press Ctrl + Shift + Esc
-Click on Performance Tab
-Look at the available physical memory while your applications are running. If the number is close or less than about 50000, then that RAM upgrade would be useful. It'll prevent any additional memory data be written on the hard drive as VRAM.
For Vista and Windows 7:
-Press Ctrl + Shift + Esc
-On the bottom right, if the Physical Memory is 85% or higher, same deal as explained in the Windows XP section.
So overall, this RAM upgrade will allow you to open more programs at a given time and give you better multitasking experience. Speed improvements happen when the RAM is faster than your current one.
"Do I have to unscrew stuff to get it in?"
No you don't need to. RAM sticks are held onto by tabs on the slot itself; so it's a matter of push in until you hear a click, or you can push the tabs on the RAM sticks. The only thing you'll need to unscrew is the case cover. But what you need to know is the RAM standard your motherboard can take. DDR1 cannot fit in DDR2 and vice versa. Also, some motherboards cannot take above a certain amount of memory. You should be fine with 1GB, however.
----To check what standard you're using, use this:
CPU-Z: http://www.cpuid.com/
It is a free, handy-dandy tool for many overclockers.
Click on the memory tab and the type is listed in the first slot.
"If I take out the old RAM, will I lose all the memory from my PC?"
No, the memory you're referring here is stored on your hard drive. We call that data.
Hope this helps and good luck.