What I do, and this is purely a personal choice:
DRAGONS:
I tame dragons in Destard. I recall in to the west side ledge in the top most level of the dungeon, and I make sure the ledge is clear of spawn. I then run down towards the center of the "main" room, where I get a Dragon to aggro on me (without aggroing it first, so it doesn't start casting on me) and I lead him towards the ledge. I really don't mind if drakes/giant serps tag along, as the drag will deal with them swiftly. When I'm coming up to the ledge, I'll precast recall and go right up to the wall of the ledge, when the dragon is near I target my ledge rune and end up on the ledge with the dragon below. Here you are safe from the dragon's magic and fire breath while you tame. I then procede to run a simple macro consisting of:
Use skill animal taming
Wait for target (editing the timeout to 1 sec)
Target by type (I change this depending of if it's a red or brown dragon that I'm taming)
Pause 0.1s
Loop, play.
At GM it normally takes me anywhere between 3 and 7 minutes to tame a dragon from all the "anger the beast" and failures. When I succeed in taming it, I take a few steps back towards the wall and hide and tab in and out a couple of times to break aggro and make sure I don't auto-defend when I run up it. Breaking aggro only takes a second, so I immediately run down, feed 1 rib to the dragon, order it to drop it's gold, and gate it out. If it is fighting drakes/giant serps, I wait for it to finish, hide and tab out again (for some reason if it's fighting and not yet blue, it might reaggro on you), and THEN gate it out. If it is another dragon it's fighting, I'll cast a gate right beside it, stand with the gate between me and the drag, and order it to come, or follow me, gating it out. I then recall back on the ledge and tame the other dragon!
If I see a red name, I run my recall macro, which stops my taming macro. I also have a hotkey to stop my macro if spawn creeps up to the ledge or I need to target a spell (if you don't stop it you'll taget the dragon, so you might end up healing/curing it and going grey).
WHITE WYRMS
These bastards are tricky. What I do is recall into the north most hallway leading to the wyrm's nest, about halfway there. I then precast teleport, and run towards it's nest. If the wyrm is on the "floor" of the dungeon I use my precasted teleport to get up on the ledge. If it is already on the ledge, I make sure I stay below it on the southern end so the wyrm stays up there and cancel my teleport target. I try to do this without wrestling or otherwise hitting the WW, as if you do, it will start casting on you, otherwise it won't and taming will be much easier.
Once there, and if it has not been hit, and thus is not casting, I run the same macro I use for dragons, and just wait it out. If it is casting, then I use a simple use skill taming/last target hot key and do it single use, so I don't target it with heals or cures. The tricky part here comes when you succeed in taming it. I do the same thing I do with dragons (hide/tab out) but WW's have a freaky aggro system, and might reaggro on you while they're still grey. Best thing is to have an invis item/tab out macro in case it engages you, because it will mess you up real fast.