Producers do a little bit of everything, actually. How much and how hard a producer must work depends on the artist.

With real bands like Oasis, they would simply guide them through the recording process and do some tweaking of the recorded songs. They also would do some mixing which means they might record each instrument and vocal separately and put them all together into one final product. Often you've seen an artist singing with earphones and no band playing. That's because he or she is singing along to the instrumentals. Recording each piece separately and putting them together often gives superior results in the final product. Producers also often suggest which songs should go on an album, which ones should be B-sides or trashed completely. Depending on how musically-talented a producer is, he may also offer some actually musical guidance. Often they are a benefical third-party in the recording process. Dave Sardy helped out Noel considerably on choosing songs and streamlining his sound for DBTT.

When it comes to garbage bands, Boy bands, Spice Girls, et al; the producer would very often be designated directly by the record label and he would do pretty much everything. Many such bands can't sing or play a note; they're simply characters hired by a label for making money off of brain-dead teenyboppers. I live in Asia and it is full of the crappiest pop music the world has ever seen. In such cases, the producers are effectively computer programmers and the artists are game characters that do what the programmer makes them do. Pure rubbish. Backstreet Boys, Spice Girls, N'Synch, and so forth. Some such artists may actually have some talent, but most do not.

The better the artist, the less a producer will likely have to do. Exceptions to this are of course when an artist needs a breakthrough or a change in sound. Kind of like what happened on DBTT. Noel needed to break out of the SOTSOG-HC zone.

Anyway, sorry to rant there a bit. Hope I answered your question. I'm not in the music industry, just a fan of music and Oasis! Cheers!