Make sure you have a safe means of access to the roof and take great care when working near the edges. If you have any doubts, or the roof is higher than single storey, get a professional. Also be sure that the roof is capable of supporting your weight.
Various kits containing special tape and adhesive are available for carrying out patch repairs, which should be done in dry weather.
Clean the area thoroughly, removing chippings and killing off any mould growth with fungicide.
If the surface is split, fill the gap with mastic before patching.
A burst blister should be dried out with a hot air stripper. You may be able to fill in the hole by spreading the warm asphalt with a stripping knife.
Allow to cool, then prime the surface of the area to be repaired with the special primer supplied.
Cut the tape to length and press firmly down into place.
Make sure the edges are well sealed.
When complete, replace chippings to protect the surface.
If this is not for you, get a quote from a local tradesman. They can often fit in minor repair work between larger jobs. It's always best to get a recommendation - have a word with friends and neighbours.