Most of the same concepts apply whether fishing with spin gear or fly gear. The terms and sometimes mechanics change, but the end goal is still the same - to get something that looks natural and yummy close enough to the fish to give them a chance to eat it. The terms you'll be looking at are as follows:
Rod Weight / Line Weight = rod power and rating. Sometimes you choose a weight based on the wind, the size of the flies being cast, and the species you're targeting. Just as a spoon will cast further than an unweighted crankbait, the heavier the rod and line weight the better it'll cast into the wind. Casting a 3oz pencil popper on an ultralight would be a recipe for disaster, as would casting a 9" fly on a 2w. Big bait = big fish = heavier rods sometimes. A 9' 6w will be good for SMB and trout. It might be a little light for some larger LMB, but it'll still land them.
Fly line ~= weights. To control depth in spin fishing you choose heavy lures, lures that have mechanisms to dive, or put weights on the line. In fly fishing, you start with a line for the depth you want to be in the water column then you can add weight to the flies to further tweak. The only 3 you'll really need to know is :floating lines for fishing topwater like poppers, intermediate line will get you just below the surface and under the waves, they usually sink about 1-2 inches per second, and sinking lines (sometimes the whole line sinks, sometimes only the tip does, matter of preference) which sink around 7 inches per second.
Strike indicator = float/bobber/etc. It wouldn't be super productive to cast a spinner into a pond under a float and just let it sit, the same is true with a fly. Generally if you're using strike indicators you're fishing rivers where the water is giving your fly action or moving it along.
Leader/Tipper = Leader. In fly fishing they're broken out for a couple reasons. First the leaders are generally tapered, with the line being heavier weight where it attaches to the fly line and lighter weight where it attaches to the fly (or tippet). The reason for this is when you cast a fly rod, you're casting the line and not the fly - which is inverse of a spinning setup. The fly line will have a loop at the end and the fly will follow it out. The heavier line helps to "turn over" the fly and push it out with the clear part of the line closest to the fish. Since leaders are tapered and either expensive or take more time to tie up, most people use another small section of leader called tippet that they just change out as they tie on more flies. Think of it as a spinning rod with braid and 6' of flouro tied directly to the braid. If you don't use a snap swivel, you'll keep cutting 4-6" of flouro off of the end every time you tie a new lure on until it's really short and you need to start over again. Instead put a small swivel at the end and tie on a 3' section of flouro, and when that section gets too short just replace it. That would be the spinning equivalent of tippet.
So now you're out on the water and you want to target some LMB, and you want to put a minnow impersonation at roughly 3' deep in the water column.
In a spinning setup you would search through your tackle box of lures to find a minnow looking jerkbait with a lip that'll get it down around 3' deep (think a rapala). You'll tie some flouro onto your braid, attach your lure, cast it out, let it sit for a second to let the splash/noise settle, retrieve slowly and let the lure create the action for you.
In a fly setup you would search through your fly box and find a nice small minnow looking streamer. Grab your reel with sinking line, tie on a 6' section of leader/tippet, tie on your fly, cast it out, wait roughly 5-6 seconds, then start retrieving the fly in short strips to give the fly action.
For you I would suggest grabbing a handful of wooly buggers in black and olive in different sizes and weights. Cone heads will be heavier than bead heads which will be heavier than no head at all. If you're fishing from shore, search youtube for videos of how to roll cast and practice a little. If fishing from a boat or kayak or standing in the water with waders, look for overhead casting and practice a little. Wooly buggers will catch trout, SMB, LMB, pickerel, panfish, almost anything. I've even caught a 10lb alligator gar on one before. Pick one fly, cast it out, and vary your retrieves until you get hit. Start with short slow strips, then long slow strips, then short fast strips, long fast strips, etc. As long as there's fish where you are, you'll eventually figure out what they want. Good luck, it's awfully addicting. I brought my brother out who's never fly fished a day in his life, and he caught ~20 rainbows and browns on an olive wooly bugger. That evening he went and grabbed a fly rod and reel and started tying some wooly buggers and the next day was catching them on flies he tied on his own setup.
If you have any questions or something I missed let me know and I'll be happy to help.