I haven't had to do one on a basic 2.0 or 2.3 MZ3 yet, but I've replaced a lot of clutches in other stuff at work... two Mini Coopers and one Mazdaspeed 6 recently.
While anything will pretty well suck at home on jackstands, after poking around underneath my own 09 MZ3, it looks like the easiest possible transaxle I may ever pull.
You've just got to get into the mindset that it's nothing but nuts and bolts... it will become much easier when you think of it like that.
Basically you want to pull everything you can off the top of the transmission: air box, battery/box, disconnect anything on top like sensors and shift cables, if there is a wire loom running along the transmission or bellhousing area, do what you can to push it out of the way so you will be able to pull the transmission straight off later on. Leave motor mounts/transmission mounts for now unless you want to drop it on your foot.
Then you want to raise it up high enough to have room to do what you need. Pull the skid plate and driver side inner fender/splash shield. Pull the drain plug and drain the fluid out of the transmission. Now you want to pull the axle shafts... to do so you need to disconnect the tie rod ends from the knuckles, the lower control arm ball joints from the knuckles, and remove the giant nut from the end of the axle shaft. Push it through and pull back on the strut/knuckle assembly so you can slide the end of the axle clear of it. *Be careful of the brake lines and ABS sensor wires, etc etc. Disconnect or remove what you need to keep from stretching them/breaking them.
Use a pry bar to pry the axle shafts out of the transmission. You may want a hand to hold the outter end of the shaft while you pry in case it lets go suddenly... you do NOT want to scratch the seal surface where it seals at the transmission. Depending on the way the shaft is, sometimes using the prybar more-so as a punch and hammering on it works better. I frankly don't know, you just gotta get it outta there.
You may or may not need/want to pull the sway bar end links at some point if they get in the way or fight you while disconnecting the lower ball joint or something.
Unbolt the slave cylinder, and if possible sling it along with the hard line completely out of the way. If it's like the MS6 I did, there was a bolt on the top of the trans holding one end, loosened that and I was able to manipulate it out of harm's way.
Then you undo the rear motor mount, then support the engine, then remove the transmission mount and bracket(s). Lower the engine as much as possible *without damaging anything on the accessory drive... watch it while lowering the engine!!!*
Undo the bellhousing bolts and pull the transmission out of there.
I use this same model at work for supporting FWD engines when possible... works very well and at home, it would leave you a lot of free room to move underneath the car if a jack was otherwise in the way.
http://www.wayfair.com/OTC-Three-Po...PA49-IOE1080&gclid=COL809isl68CFYMKKgodIkCUyQ
Here it is supporting the MS6:
On the MS6 I had to drop the entire crossmember, but that I think is because the 6spd is freaking massive. Just eyeballing it, it appears that I could get away without doing that on my MZ3. Also the MS6 was AWD so there is a bit of extra crap in the way that had to come out first.
This is also from the MS6, but you can get an idea of all the stuff that needs pushed out of the way(wiring and coolant hoses and stuff)... there is nowhere near as much on a non-turbo 2.0 or 2.3.
Good luck!