This is the sentence that you want to negate:
Ich gehe abends oft aus.
I often go out at evening.
There are two possible positions to insert »nicht« to negate the sentence. It's before »oft« and behind »oft« (same in english):
Ich gehe abends nicht oft aus.
I don't often go out at evening.
This is the most usual way. But there is also a second position where »nicht« is allowed:
Ich gehe abends oft nicht aus.
I often don't go out at evening.
In this second case you often want to at some additional information:
Ich gehe abends oft nicht aus, weil ich es mir nicht leisten kann.
I often don't go out at evening because I can't afford it.