Mining

Branch mining is the most efficient. There's a mathematical analysis on it in the official forums (the link is to an archive of the post).

Here's a brief description of branch mining:

• You dig down to the bedrock, because that's where you're going to find the most different kinds of stuff.
• One or two layers above the bedrock, so you don't have it interfering with your work, you dig a long tunnel, 2 high and 1 wide, which will serve as the trunk.
• Then, every 4 squares on either side of the trunk, you dig perpendicular tunnels extending out 20 blocks (or as far as you want).
• You leave 3 undug blocks between because veins are generally 2x2 horizontally, so you will see ore in the vein even though there is technically one row of unexplored blocks.
• When you finish that layer, you can start one a layer above, offsetting the branches by one block so that you are more likely to find veins you could possibly have missed the first time.

So essentially, a long hallway (the trunk) with perpendicular hallways (the branches) coming off either side.

██▒▒▒▒▒▒  ██ blocks you should mine
██▒▒▒▒▒▒  ▒▒ blocks you can see
▒▒▒▒██▒▒  __ blocks you can't see if you don't mine ▒▒ blocks (there's none!)
▒▒▒▒██▒▒  Repeat this pattern as many times as needed

From a head on view

Travel

As with any mine, travel is most easily accomplished using minecarts.

You can place a booster to get your cart traveling at max speed in a short distance so that you can make the trip up quickly, and you can even attach chests to mine carts to carry all your findings from the mine up the track very quickly.

Short of minecarts, make sure you're using stairs and ladders to their fullest potential. You don't want to be jumping up one block at a time all the way from your mine to your base.

I made a pretty quick and dirty XP farm as such:

Find a zombie spawner, punch out all the blocks around it, leave 3ish blocks of space all around it, making a big dark room around the spawner.

Put water source(s) at one end of the room, pulling every zombie that drops to the other side of the room. Make a 1-wide hallway for the water to flow into. Where the water stream ends, put in a 1x1 vertical shaft for the zombie to drop down (place this RIGHT AFTER the water, don't let water flow down the hole).

Make the bottom of the "tube" out of glass so you can see the zombies inside the "kill zone". Leave a single block at the bottom so that you can swing your sword at the zombie's feet.

I made my vertical shaft high enough to take away ALMOST all the zombie's health. If the fall kills them, no XP bubbles. I got mine to the perfect height that I can 1-shot all the zombies with a stone sword (you wouldn't believe how fast this goes through swords).

Hope my description isn't gibberish, I'll get some screenshots later if this isn't clear. =)

                          |
                          |
   S   <-zombie spawner   |
                          |
                          |
WWWWWWWWWWWWWWWWWWWWWWWWW | 
                        | |  <- vertical shaft - experiment with height
                        | |
                        G G  <- glass
                        G G
                             <- air for swinging sword
                    xxxxxxxx <- floor