Don't judge me, I don't do a lot of this, but I very rarely ever use anything like RAM addresses and all that mumbo jumbo.
I don't really understand how that stuff works.
By the way, I just signed up for this site in case you didn't know.
Speedrunning or tool-assisted speedrunning?
The former is easy. Just play the game normally.
Tool-assistance allows abuse of any emulator feature that doesn't change the way the game runs (cheat codes, ROM hacks, etc).
Have you checked out the resources in the main Wiki yet? Maybe try starting at this page?
but I very rarely ever use anything like RAM addresses
As to why RAM addresses are important:
The game may not show something accurately enough:
Example 1: the gauge on screen might have 10 steps, even if game internally keeps track of 30,000. Good luck finishing with 1 unit remaining (which might very well be the fastest way) if you don't have the more accurate view.
Example 2: Less than one pixel position differences can affect things greatly (e.g. can make or break some almost impossible jump). But such differences won't show up on screen by definition, since 1 pixel is the smallest displayable amount.
Even if things are shown, numbers might be easier to read/understand:
Example 1: Character normally runs 6 pixels per frame, but slows to 5 pixels per frame on slopes upward. This is somewhat difficult to notice, but blatantly obvious if one is watching how character position is changing.
Something important is not shown at all:
Example 1: You are shooting at a boss. Is it really taking damage or not (the boss might be shown taking damage even if it isn't).
Example 2: Does the randomness in the next segment differ from what I have already seen, or is it the same? Good "randomness" may very well be much faster than bad one.
Example 3: Car speed oscillates between some values, but there is a trick that allows freezing that oscillation to the fastest value. This might very well save lots of time.
In summary, watching the values of RAM addresses can make it much easier to compare your current performance to past ones (is it better or worse?) and make it much easier to make a good run as you don't have to guess as much.
