Well it depends on the style of roof you are putting back in. Usually it is an asphalt or fiberglass matt shingle you will install. Just like the ones that came off.
1. Remove all old roofing and tar paper.
2. Check all boards or plywood for damage and nail down loose boards. Any replaced boards will usually cost extra because that is more work which was not visible until the shingles where removed.
3. Install new metal drip edge at the bottom of the roof, this is the stuff that lets water run into the gutter. Install Ice and water membrane at the bottom 3 feet of roof and in valleys (where 2 roofs meet).This is basically a sticky rubber membrane to keep ice dams and water from coming into the attic space. And last, install a metal rake edge at the side edges or ends of the roof to hold down the tar paper.
4. install any boots over pipes which protrude out of the roof for plumbing or vents out the roof.
5. Install the new shingles, which you picked.
6. Install any metal flashings for chimneys or skylights.
7. Install any ridge vent and soffit vents to complete the system if it needs it.
These are the things usually included.
If you post a pic of the roof and what the roofer comes up with we can look at it further.