If you've been doing ILS approaches already, then you have, in essence, been doing a VOR approach.

Think of an ILS without a glideslope and then lessen the sensitivity. Instead of a glideslope indicator, you descend at certain points, which are determined by DME distance, crossing a VOR or NDB station or a radial associated with another VOR transmitter.

You begin the approach just as you would an ILS.
You center the course needle.
Maintain a certain, specified altitude.
A non-precision(VOR/NDB/GPS/RNAV) approach with DME is the easiest.
Instead of waiting for a Glideslope needle, you wait for a certain DME distance and descend to a lower altitude(stepdown).
There may be several "stepdowns" but the final step is called the MDA(minimum descent altitude).
When you have reached the MDA, you can't go any lower until you see the runway.
If you reach a certain DME distance and STILL don't see the runway you have to discontinue "go missed" and try  it again.