The first two answers are on track.
One more critical thing you should know is to mix water into your drywall compound, assuming you are using pre- mixed, in order to achieve the thin coats already described.
Thinner compound will go on much more smoothly than just using it right from the bucket.
Smoother coats of compound mean less sanding.
To apply your compound you could probably get by with a 4" putty knife for corners and an 8" knife for the rest of your joints.
Prime with PVA primer only after all joints are sanded smooth.It is really difficult to try and sand back over something that you've already painted. Always wear a mask when you sand.
This is a skill that takes a few years to get good at but give it a try.
Professionals generally use paper tape although the self stick kind is acceptable for a DIY project. If using self stick you skip the first mud bed and stick the tape directly to the wall ,then proceed with the next three coats.
If using paper tape do your corners first.Tear tape from the roll in the lengths you need to tape your corners.Fold the tape in half lengthwise.
Apply a thin mud bed with you 4" knife then lay your corner tape in the mud bed. Press and smooth the tape down w/ your 4" knife . Do your remaining joints in the same way with the acception of folding your tape.
Let it dry for a day.
Next day apply a second coat of compound.Let it dry for a day.
Next day, sand lightly as needed.Try not to sand so much into the paper the you cause it to "fuzz up". Apply third coat.Let dry another day.
Next day, sand smooth.Wipe any sanding dust from the walls.Clean all dust from the floor.Prime w/PVA primer.Then paint what ever color you want.
A side note as far as sanding goes, Some people have good luck in small areas such as closets by wet sanding.You might try it if the dust caused by the traditional sanding method bothers you.
Female builder / remodeler for 29 years