The word that Pastor Thieme coined to describe the process of regaining fellowship is "rebound," because it's a quick word that not only encapsulates the entire process but provides a nice visual as well: when you get out of fellowship, you've fallen on your face spiritually speaking, and are basically lying there on the ground during all the time you spend in the power of your flesh. But with God's grace provision in place you can quickly bounce back up and get going again -- you just 'rebound.'
The word for confess in I Jn 1:9 is "homologeo" which means to name or to cite a court case (that would be the indictment of the justice of God against mankind as sinners, and the penalty of spiritual death, which Jesus paid on the cross in our stead). To do so you just admit that you did the sin. You name it. You acknowledge it. It's a sin. Jesus paid for it.
And you're filled with the Spirit again. Simple.
The reason I like "rebound" better than "confess" is because confess seems to imply feeling sorry, or bad about the sin, or doing some sort of penance to make up for it. If that were needed, then Jesus's work would not have been enough. But it was. We don't have to do any penance. Penance or feeling sorry isn't grace.
You don't have to make a big production out of it. You just name the sin. (You certainly don't have to promise you'll never do it again, because odds are you will, and now you have lying and thinking more highly of yourself than you ought to, to add to your list of sins to confess). It's incredibly simple for us, though it wasn't at all for Jesus. Every sin we name He already bore, and all the one's we're going to name as well. He did all the work. We receive the blessing. That's what grace is all about.