Think of it this way, if you have both hands on the handles, the part of the bit closest to your right hand will be moving toward you. That should help you visualize the rotation of the bit, so you are always moving the router so the bit is going forward on the side that is doing the cutting, against the cutter's motion.
If you are making a dado or a groove, use a straightedge, and move the router as if you were cutting a shape on the straightedge.
This helps me get through my routing day.
I'm not slow, I'm pacing myself!
Isaiah 44:13 Another shapes wood, he extends a measuring line, he outlines it with red chalk. He works it with planes and outlines it with a compass...
Usual kit: Table saw, band saw, dual base router and table, lathe, various saws, planer, sanders, and a multitude of hand tools.