Well, one of the reasons they tell you to get it cleaned right after the wedding is that sweat and champagne stains are easier to get out when fresh. Also, garments that you want to keep long-term shouldn’t be hung up, shouldn’t touch non-archival plastics, shouldn’t be folded, should be protected from light and moisture and vermin, etc.
As for appropriate cleaning and preservation now, the best route is with a professional garment preservator who is experienced in dealing with wedding dresses. Obviously, this can be expensive. It’s your call. Try and get a reccomendation from other people who are happy with the way their gowns came out - you don’t want to take your gown into an inept preservator and have it come back missing sequins and beads, for example.
If you choose not to have it specifically taken care of by an expert, here’s what I’d do: look at the label. There’s tons and tons of kinds of wedding dresses. Some can be hand-washed or dry-cleaned, while others can’t be dry-cleaned because of the decoration on them. Hopefully the label will tell you this, but you may have to ask a reliable dry-cleaner’s advice. At the very least, get that spot out. Make sure you get any sweat stains out, too. Be sure to check the train for stains carefully, if there is a train. You want the body oils off the thing, but you may want to air the dress out after cleaning if it has a strong smell or anything.
Check it and make sure there are no metal pins or staples (heh, instant alteration) or anything in the dress. This is also a good time to check for loose stitching, loose zippers, that sort of thing. Gently stuff the dress a bit to get it to keep its shape with acid-free tissue paper, and put it in a full length acid free cardboard box. Store it in a cool, dry place that hasn’t got bugs and rats and things in it.
Do not store textiles that you want to preserve in a cedar chest without at least an acid free barrier between the wood and the fabric. Do not store it in plastic, especially not plastic of unknown composition. Do not just pack it away and forget about it - check on it every year or so to make sure it isn’t getting mildewed or discolored or anything. Do not store it in your attic or basement where there are large variations in temperature and humidity.
That’s all I can think of off the top of my head. Honestly, I’d have a professional clean it and box it, but make sure you get somebody good. If it’s worth keeping, isn’t it worth keeping in good shape? This is all important particularly if you entertain notions of keeping it as a heirloom for use in future weddings - I’ve got my grandmother’s wedding dress, complete with her authentic sweat stains.