I would not recommend a DIYer wet the brick or the wall. If he is a smudger, then the damp wall and brick will atract the compo and be stained much worse when it all dries.
Mix the compo but not too wet and use a plasticiser (fairy liquid) which will reduce the water content and keep the water within the compo.
Slide the compo for the bed joint into the wall - put it on the big trowel and then slide it in and flatten it to 15mm with a pointing trowel.
Then butter the perp joints - again with the pointing trowel. Make this more of a wedge, so that there is about 15mm of compo at the back, and 5mm at the front.
Now, with the brick to be inserted put compo on the top and fill any frog or holes. Flatten this to a wedge shape - 10mm at the back and 5mm at the front.
Then put some compo on the perp joints , only this time do it the opposite - 5mm at the back and 10mm at the front.
Now wait a bit until the brick absorbs the moisture and the compo has dried - not bone dry, but so that there is not much moisture visible, and its a bit firm to touch.
Then with two hands slide the brick in - keeping it more to the top of the hole. When its half way in, take a hand off and scrape any compo which is about to drop with the trowel. Then push the brick in, and more downwards to its correct height. Scrape any more loose compo off. Cut this off cleanly, and don't smudge it up the wall
If you need to align the brick, then push the trowel into the joint and press it down on the brick.
Do any final adjustment with your fingers.
If you need to correct any lopsidedness, then poke some little pieces of brick into the joint to lift the brick. Leave these in while you repoint, and then either pull these out or push them in more and finish the pointing
For repointing, don't use wet compo. Use semi-dry - put some on a brick to dry it out if need be.
Flatten this on the big trowel to 10mm, so that it is joint size and you wont smudge it up the wall, but rather it goes into the joint
Phew - there must be a video on utube or something