Actually it's entirely up to you. Some players prefer the bridge tight to the body, maybe with all five springs installed. When you bend a string, the bridge won't move. If you use the trem, it's not very easy and you can only dive, no pull-ups. The tuning is more stable this way but I think it sacrifices the subtlety that Leo's design permits.
The factory spec is for the bridge to float, which I prefer. I use three springs but first loosen the springs by backing out the two trem claw screws. Then use a wedge of wood temporarily jammed in behind the trem block to hold the bridge steady so it's floating 1/8" above the top of the guitar, measured at the rear of the bridge plate. Then tune to pitch. With the bridge floating, it will raise your action, so adjust your saddle height and then readjust your intonation. Finally, start to tighten the two trem claw screws until the string tension balances the string tension - at that point the block of wood will fall out and you're done.
Here's another tip for a two-point American Standard type bridge: set the saddle heights so the high and low E strings are very close to the bridge plate,with the low E raised a little more than the high one, and adjust the middle four saddles to conform to the fingerboard radius using a homemade 9-1/2" radius gauge (cut out a piece of oaktag along the arc of a 19" circle, or a 9-1/2" radius). It's most accurate if you put the gauge under the strings instead of over them. You'll only have to do this radius adjustment once with an Am Std bridge. From then on, all your action height adjustments will be made by turning the two pivot screws and the radius of the saddles remains the way it is - it's more like adjusting a Gibson tune-o-matic for action height and you won't have to worry about tweaking twelve little screws anymore.
Not sure it actually does what it's advertized to do if a string breaks but the Trem-setter is a nice gadget for getting the bridge back to pitch. They are finicky, however, and unless you want to decipher Hipshot's instructions you might want to have it professionally set up. You'll recognize the Hip Shot right away if there'a a gizmo with delicate springs and knobs and a rod running inside it, connected at one end to a hooked plate screwed to the bottom of the spring cavity. With a Hip Shot installed, there are two separate spring claws (one on each screw) rather than a single claw with five hooks held by the two big screws.
Now, as for tone, some people will tell you that you get more sustain and coupling with the bridge tight to the body and I have not found that for myself. If I were cynical (and I am) I would say that it's done by techs who are making an excuse for doing it the lazy way - on the other hand there are those who understand the difference (based on trying it both ways) and who are entitled to ask for it to be set up a given way. Stevie Ray Vaughan was a five-springer with the bridge tight to the body, so far be it for me to criticize the choice. To my ear (which can't hear the difference anyway) it seems that whatever difference there might be does not outweigh the benefit of having the trem floating if that suits your style of playing.