This project shows you how to finish drywall at inside and outside corners.
Covering corner bead at outside corners is easy because the bead itself guides the drywall knife. Run one side of your knife along the bead to produce a smooth, flat joint as the mud covers the nailing flange. As with other joints, apply at least three coats, sanding in between to feather the joint where it meets the drywall. The bead itself isn't hidden in mud. Simply scrape excess mud off the bead, then paint it along with the drywall.
Inside corners are more difficult. They require taping and mudding. The hard part is smoothing the mud on one side of the corner without messing up the mud on the other side.
Resist the temptation to try to get these inside joints perfect on the first, or even second, coat. Accept that there will be ridges you'll need to sand or knock off in the first two coats. To avoid ridges on the third coat, think of it as a filler coat; press hard on the knife so you fill imperfections instead of leaving behind a thick layer of joint compound. Remember there's no law against going over the joints a fourth time if necessary for a smooth finish.