How to make a coil to be resonance?

Every coil has a SRF (self resonant frequency) but you
may not like where it is. Usually people try to stay below
SRF when they care about inductance as a value.

A low frequency self resonant coil needs high inter-turn
capacitance which may be unlikely.

You could of course put high-Q capacitor across the
entire length, or distribute caps along the winding. You
could even conceive of making them part of the structure
if the wire is bare and the caps don't space the windings
unacceptably.

The electrical length of the wire in total is your other
source of resonance, time-of-flight. This is the Tesla
coil's deal. 1nS per foot or thereabouts, you might not
find this lands where you like if you wound the coil first.
If it's 250 turns and 4" circumference, that's maybe
1MHz-ish (consult your local Tesla coil construction
expert, he ain't me).

It already have a natural resonance frequency; because of internal parasitic capacitance. You can either measure it directly or estimate it indirectly.

You have made an inductor; it needs some capacitance to be self resonant. You can put an external capacitor in series or in parallel and tune it for a desired frequency.

You can estimate the inductance from tables (geometric considerations of the solenoid) and also estimate the intrinsic capacitance.

To turn this into an active oscillator, you need an active element (e.g., a transistor) that can provide some gain to overcome losses and provide some measurable output. Without that, it is just a helical coil with a natural frequency determined by its geometry.

To achieve what?