Well, it depends on when you are doing the cleaning.
a). Between dives?
b). Last dive of the day?
c). Last dive of a trip?
d). Last dive before putting it away until the next time you dive, whenever that may be?
You may get a lot of different answers - but generally, the further down the above list you go, the more you want to clean it.
Between dives - maybe you're just rinsing off computers and cameras (or their housings).
Last dive of the day, maybe you give everything a quick once-over on the outside, and turn it inside out to dry and/or give air exposure to reduce stink.
Last dive of a trip, maybe you get everything a quick once-over, inside and out, and make sure stuff is mostly dry before packing it up for the trip home. Once you get home, you give everything a GOOD once-over, inside and out, and make sure it is perfectly dry before packing it up for storage.
Last dive of a local dive event, maybe don't worry about it at the dive site, and you give everything a good once-over, inside and out, once you get home - and make sure it is perfectly dry before packing it up for storage.
I'd recommend that, when possible, you rinse with running water, rather than just soaking. If you just soak, you're just making a salt water solution for it to soak in (assuming you were diving in salt water) - that's not a big improvement over doing nothing. In the winter, I use my shower to rinse stuff, and in the summer, I do it in the yard with a garden hose.
Rinse the inside of the BC well - swish the water around, dump it out, fill it up, swish, dump, etc. The inside of the BC is probably what I concentrate on most. Some people use a special solution additive to prevent mold or reduce stink, but I don't. I let my stuff dry with the dump valves completely off - and hang everything in the garage for a while until I know it is dry (getting the last bit of water out of the BC can take a while). Only then do I pack it away for storage until next use.
Rubbery parts do not like ozone. Do not hang or dry near ozone sources, such as near boilers, furnaces, hot water heaters, etc.
Rinse regulators while attached to tanks with an open valve when possible. Personally, I don't like to soak my regulators when cleaning, I definitely wouldn't do it without an "active" tank attached. Don't push the purge valve when soaking if you do not have an active tank attached. If you rinse off tank, be sure not to soak or get water into the tank-end of the valve on the first stage.
Do not hang on "thin" things that can leave a crease. A 2" wide PVC pipe makes a good thing to hang things on. I made a little contraption for use in my garage that works pretty well. I'll attach a picture. Note the use of the end-caps to keep the pipe from falling off the hooks. Note that I can easily remove plastic pipe and bring it down to put things on it, and then hang it back up. Note that it is high enough to allow a wetsuit or drysuit to hang completely, without touching the floor. If you wanted to, you could have a similar pair of hooks hanging from something outside, hang your suits or BC or whatever, and give it a good hosing down - and then bring the pipe back inside and hang it up for it to dry without direct exposure to sunlight, thieves, animals, alien beings or other such things.
Store in a sealed container, such as a large rubbermaid tub with a top on it - inside, under normal temperatures. Put dive computers and other such things in a safe or other secure area. Record serial numbers and get a "personal articles policy" on your stuff as needed.
Cheers!
nd