After your mead stops bubbling, you'll need to rack it into either another bucket or a carboy. I like it in a carboy because you can see it in all its loveliness. If you want to drink it strait from a tapper bucket, you could just rack it into that. The purpose of racking is to get all the sediment (dead yeast, old fruit, etc) out. You want a clear product. Racking it can get the yeast going again, so you'll want to leave it in the second racking (carboy or bucket) for awhile again. Otherwise, you could use potassium sorbate if you want to stop it (but I generally don't add it). However, if you decide to bottle it and it's still fermenting, there's the potential to blow the corks out or the bottoms off, or maybe it might just be fizzy. (If you have bottled some and the corks are leaking honey, or some have blown, then you'll want to put them in the fridge and drink them quickly.)
First, sanitize all you equipment.
If you had a bag or fruit in there, remove the bag or as much of the fruit as you can with a straining spoon. Save your fruit for smoothies or something. Now, take your siphon tube and get it going. You can either get a pump one or one that you have to start the suction yourself. (This is a great time for a taste test). Allow the mead to flow from the bucket to the carboy, avoiding letting the sediment from the bottom get into the tube by pulling out the tube when you've got as much of the clear mead as you can in the tube. Put the airlock back on and allow it to sit for awhile again (a month or two or however long it takes you to get to it).
Only one more step until you are enjoying your home brewed mead.