There's different ideas about the best way to do this. I think good cleaning before reassembling is a good start. But I think that way about everything. Things just seem to work better and look nicer that way, don't you think?
I would make sure the outside edge of the tub cover is clean and mineral free. SOS pad or green scratchy pad and soap, then rinse. Is there any mineral build up there? If so use some CLR or vinegar and get that off until your down to clean porcelain. Same goes for the inside edge of the outer tub and the flange at the top edge of the tub.
If there's any rust on these areas, use some medium to fine grade emery paper to remove it. Wipe the areas and let them dry thoroughly. Then these areas will have to be patched to stop further rust. I like JB Weld. The two tube kind. One tube is red (hardener) and the other black (steel). Mix equal amounts from the tubes onto a piece of cardboard and mix with a toothpick until it turns grey. Apply enough to cover the damaged area(s). Then spit on you finger and smooth the JB down until you get a perfect even repaired surface. Let dry for 24 hours in a warm dry room. After that you will have a nice repair that's almost as nice as the porcelain. If your porcelain is perfect, I've wasted a paragraph.
Next, how's your tub clamp? Make sure it's clean and rust free. Use some WD-40 or light weight oil and some steel wool to clean it, then wipe it down with a rag. If it's really bad you might consider replacing it. I've never had to, but some have. Make sure it's not bent. Also make sure the screws on the clamp are working well. Put some 3 in 1 oil on them, screw them both all the way together and apart and wipe off the excess oil. If the screws are rusty, this will help clean them and get them working well again. A spray with WD will rinse away the rust particles and you can reapply 3 in 1 again.
Clean your rubber tub seal well, making sure there isn't any rust bonded to it. You can scrape it lightly with a dull knife if needed to remove rust or debris. Just don't cut it. After it's clean, take a rag and spray some Pledge into the rag and pull the seal through the Pledge soaked rag until it's well coated. I have even soaked old rubber parts in Armor All or similar type product if more drastic treatment is needed. Put the rubber parts in a big pot, pour the product over the rubber parts until all are covered, put a lid on the pot and place in the oven at around 150-175 degrees for 24 hours, remove the pot and let cool, take out the parts and wipe down. This usually rejuvenates old rubber parts if they're not to far gone. This usually isn't needed for the tub seal though. It's pretty durable.
Next, take a rag and spray a good amount of Pledge onto it and wipe down the outside edge of the tub cover and the inside edge of the outer tub. This will help the two parts slide together easily. Then slip your rubber tub seal over the top of your tub cover. Pick the smoothest sides of the tub seal to place against the tub cover and toward the tub lip for the best seal. It's a triangular seal and can be turned so the best sides are against these two water sealing surfaces. Next, install the tub cover on the tub with the off balance flange straight toward the back of the machine. Consider this the 12:00 o'clock position. Now lower the machine top down and adjust the tub cover to machine top clearance. It should be close but not touching all around the circumference of the opening. A 1/4 inch to 3/8ths is about right. Comfortably close but not touching. After you get the adjustment right, raise the machine cover again. Put your hand between the inter tub and tub cover and gently slide the tub seal down the tub cover until it seats between the cover and the outer tub flange, making sure the tub cover doesn't move or your tub cover to machine top clearance will no longer be right. The silicone in the Pledge will help you slide the tub seal down without moving the cover. Lower the machine top down again and check your clearance. Press down on the machine cover front and grab the agitator and move the tub around to check the clearance. If it's not rubbing and it looks even all around you're good. Always remember - this is your final tub cover adjustment. If you move it or bump it you will have to adjust it again.
Now raise the machine cover again. Take your tub cover clamp and assemble the two halves. Just a turn or two of the screws should be enough. Put the clamp over the tub where the flange and seal are with the screw adjustments at the two o'clock and 8 o'clock position (back right-hand corner and front left-hand corner. Now start tightening the screws. Go back and forth to each corner and tighten each screw equally. This is especially important as the clamp starts to get tighter. It keeps the tub in round. As you slowly tighten the screws you will see the clamp closing over the flange and seal and they will disappear from sight. Get the clamp good and tight. If all goes well you should now have a water tight seal. If you have a good tub seal that's not damaged or creased this should work. I've heard of people using silicone sealant on leaky spots on the seal when they can't get it to stop, but I've never had to do this. This can be a tricky and sometimes frustrating process, but if done properly it usually works. Good luck.