To correctly tape drywall, limit the number of seams, use self-adhesive mesh tape, avoid overlapping, and use corner protectors instead of tape on the corners. Correctly mudding drywall involves patiently applying it in three or four coats, using premixed joint compound of the right consistency and applying it with the appropriate taping knife.
To avoid a lumpy look, limit the number of seams by using the largest drywall pieces available. Make sure that all screw heads are below the surface of the drywall, and then cover the visible seams with self-adhesive mesh tape, avoiding any overlapping. Do not use the tape on corners, but instead use plastic or metal corner protectors on the outside of the corner, and use pre-folded paper tape inside.
To properly apply joint compound, apply several thin coats instead of one thick one. For a smooth, lump-free finish, use pre-mixed compound instead of dry, powdered compound. For the first application, stir the compound, and use a flexible, 6-inch taping knife to apply the compound directly over the seams. Switch to a wider, 12-inch taping knife to smooth out the compound, wiping it flush with the wall. For a clean look, wipe off excess compound after each pass with the knife.
Allow the compound to sit for 24 hours before applying another coat.