Help Switching Hard Drive

I recently recieved my brothers old computer, and I switched over my graphics card and added an extra stick of ram. Im just wondering if there is a way that I could transfer my old harddrive to this computer, or some way I could transfer the data from my old computer to this one and somehow save the information on this computer just in case.

Btw, The computer isnt recognizing my extra ram, is there anything i have to do specifically to do so?

to get it on a cd, you need a cd burner, a cd cant hold much data, so you actually need a dvd burner and dvd's. dvd's are like a dollar each and can hold 2g each. so youll need a lot, dvd burners are like 20 bucks.

 you could get a usb flash drive to transfer data, like 2gb one for 20 bucks about

you could buy an exclosure which allows you to put a harddrive in it and connect it to another computer and transfer all the data from one harddrive to another, theyre about 20-30 dollars

those are your 3 options.