Branch Mining is one of the most popular techniques. It involves mining down to the Y=15 co-ordinate and ‘branching’ out covering every single block so you can see any and all ores.
To begin your branch mine you should mine down to Y=15, (This is best found on your map). Get down there by any means you like. The way i’d suggest is to mine the block in front of your feet in a staircase fashion all the way down. Do this in a 2×2 block area.
Once you get to the layer Y=15, mine out a 5x5x3 room, (that’s 5 wide, 5 long and 3 tall). This will be you base room, I would equip it with a Crafting table, two or three Furnace’s and two double chests.
Mine out of this room in the middle of the 5 block long wall. Make this shaft as long as you like, it really doesn’t matter. Then mine on the left side of this shaft every 4 blocks as to see every single block in the wall.
Repeat this on all four walls of your base room. it should look like this when you are done: