What is the most cost effective way to repair a roof?

What is the most cost effective way to repair a roof - underboards and all?

Well, the roof type in question is really the deciding factor, then the pitch of the roof, and the weather you are working around. The plywood underneath the shingles is going to be spendy to replace and you usually want to tear off tiles or shingles back to a point where a whole sheet of 4'x8'x3/4' ply can be exposed and replaced. The method of doing this will differ depending on the factors I listed above.

Tile roofs have furring(sp?) strips that are used to raise the area where a nail is put into the solid tile. Some of these nails can be quite expensive depending on how long you are looking for it to last. Composite roofing with 'tear off' tiles are much easier and can be repaired and replaced easier having no furring strips and using much more common nails.

The easiest and cheapest quick fix for a leak would be to buy some wet/dry roof cement and start covering areas you believe are leaking.