I know you can use ps to view running processes, but can you also see which ports are being used by the processes?

i'm still not as familiar with it as i'd like to be, but lsof is one way forward here. it can give a LOT of info though, so you'll need to whittle down what you are asking for.

The primary tool for getting this info (the one that exist in all distributions and all versions of them) is netstat
But there are other tools as well.

I will mention what to run in order to see listening ports and ports used by established connections.

a: netstat -lp
-l means listening
-p means pid (of process)
also
-n means numeric (don't show hostnames)
-t means tcp
so if you want to see only tcp ports you run "netstat -tlp"

If you don't use "-l" option then you see already established connections.

b: fuser
fuser can be used to see which process uses a port
the syntax is very simple. you run "fuser port/protocol"
e.g "fuser 25/tcp" will tell you which process uses port 25
It doesn't show you all the processes/ports like netstat

c: lsof
lsof -i

if you just run "lsof -i" you will all the ports (listening and established)
if you want just one port you run "lsof -i TCP:25"

I tried to put only the simplest syntax. You can put a wealth of other options as well (especially for lsof)
If you read the manpage of these tools there are more options

lsof produces the most pretty/readable/understandable output and nowadays exists in all major distributions, but i mention the others
too for the rare case that lsof doesn't exist.