Is tape applied to drywall right after mud is applied or after it has dried?
Paper tape you apply mud first then bed the paper tape with mud still wet.


Apply a thin layer of mud slightly wider than width of tape
Lay tape over seam
Scrape the paper tape with a taping knife to bed the tape. A thin layer of mud will cover the tape in the process.
Feather the edges of the mud with a wide knife (10" - 12")
wait until dry and scrape down any ridges or unevenness with the taping knife
Apply a wider layer of mud over top and smooth it out and feather the edges.
Preferably repeat steps 5 and 6.


Fiberglass tape you apply before any mud.

Edit: One more tip....

For small patches like that I usually only worry about feathering the outside edges and will feather it out that edge to the width of my largest knife (12" I think.) When I'm done with that edge and everything is dry I'll come back and fill in the entire inside area over the patch with mud and level it out to the height of the mud over the tape. It makes the repair less noticeable. Instead of having a large outline of a rectangle of raised mud you have a square that blends in better.