Way of the Force
The primary requirement for advancing to higher levels is experience.

How much experience you need for each level is unpublished, but you can
tell in various ways if you already have enough experience for your next
level and if not, how far off you are approximately.

First of all, when you pass the experience requirement for your next
level, it will be indicated by the score command. Its output will
contain an extra line saying that "You feel very experienced".

The second way to obtain information about this is by going to the
advance room and checking the cost of advancing.

There is an approx 5:1 relation between required payment and lacking
experience, so you can tell how much you will need approximately.

Since skills (specifically bargain) will influence the price somewhat
this will give you an indication, but will not tell you exactly how
much you need.

An indication of what you need for the first few levels and for level
20 is provided here to give you something to aim for:

level 2 : 580
level 3 : 1111
level 4 : 2464

...

level 20 : 2000000

Upto level 16, you will get a new force technique every second level.
Thanks to those force techniques, equipment becomes less and less
important when your level increases. A level 15 player for example
does not need anything other then a few heals to start playing, whereas
a level 5 player really needs a decent weapon and armour. Luckily low
level players are provided with starting equipment. Higher level players
are not.