First off, memory (or RAM) is ENTIRELY separate and different from storage (your hard drive).
Second, RAM is ALWAYS internal; it is mounted directly onto the motherboard, usually in sockets.
Now that we have that lesson in basics off our chest, you should know that RAM is usually pretty easy to replace/install. I say “usually” since Apple sometimes likes to make things difficult with their all-in-one designs that intentionally block end-users from upgrading/modifying/repairing their systems. Some models are easy to get into though.
So we need a little more information. In order to help you, we need to know which Mac you have. Not only do we need to figure out how hard it is to upgrade, they also use different types of RAM, so we need to make sure you get the right type.
It is obvious that you have an older model, since no Mac made within the last 2 years has 10.4, and it’s been 3–4 years since they made one with only 512MB of RAM. In fact, it is questionable whether installing more RAM will help much as most Macs (and PCs) of that vintage are at least two generations behind in processing and graphics, and may not even be able to run the latest software.
It is safe as long as you have the wisdom to know when to ask for help instead of assuming you already know, the intelligence and courage to follow instructions, and the dexterity to tie your own shoelaces. backing up your hard drive is not required for upgrading RAM, but it’s always wise to keep an external backup anyways just in case your hard drive goes tits-up.