At it's most basic, needle felting is just stabbing roving (unspun wool) to tangle it into matts in whatever shape you want. Stabbing the wool works because the needle has little barbs on it (if you run your finger along the end of the needle you can feel them) that grab and tangle the wool.

Supplies

Roving for the body
Roving for the head and nose
Roving for the hat
Roving for the beard
Felting pad (piece of foam, sponge, pillow you don't care about, pouch filled with rice. Just something you can put your piece on and stab into)
Fine felting needle (40 gauge is my preference)

Step 1: Make the Body

Grab some roving of the colour you want the body to be.
Wrap it around your index finger a couple of times. Remember that after felting the body will be smaller and shorter than it is around your finger.
Take it off your finger and place it on your felting mat.
Poke at it while turning it. At this stage we're not really trying to shape it, just get all the wool secured so it doesn't easily come apart or unroll. Once you can take your piece off the matt and not have any loose pieces sticking out, you're ready to move to the next step.
To felt the bottom and the top, grab some of the roving with your needle and poke it down on the other side. Essentially, you want to fold a little bit of each side over to ensure you get a nice base.
Keep poking at it till you get the shape and firmness you want. Remember, you can hold the roving in the shape you want it to be with one hand and stab with the other.

Step 2: Make the Head

Grab some of your skin coloured roving. It'll be a bit less than you used for the body.
Again, wrap it around your finger to roughly form the shape.
Take it off your finger and poke at it while turning it around on the felting pad.
Keep stabbing till it's the shape and size you want.

Step 3: Make the Hat

Same thing again, grab some roving the colour you want the hat to be, it'll be a similar amount to what you used for the body.
Wrap it around your finger and then poke at it on the mat so that it doesn't unroll.
Pinch one end of it between your fingers to form a point. While holding it in that position poke the roving to keep it in that shape.
Stab away till it's the shape and size you want!

Step 4: Attach the Head to the Body

Hold the head on top of the body.
Point your needle diagonally so that it goes through the top of the body (grabbing some of that wool) and into the head.
Go around the head felting like that to help secure the head.
Now go from the top of the head straight down to the body. You don't need to bring your needle all the way back out since we're not trying to shape the head, just tangle the head fibers with the body ones. When you do this, think about where the barbs are on your needle and make sure they are going deep enough to go into the body.
Keep stabbing till the head is securely attached!

Step 5: Attach the Hat to the Head

Position the hat where you'd like it to be on the body.
Felt around the rim of the hat to attach it.

Step 6: Add the Nose

Grab a small amount of the skin coloured roving.
Roll it between your palms to roughly form it into a ball.
Stab it into a ball!
Stab it onto the head!

Step 7: Hair on the Back of the Head

If you have a bit of space behind the hat where the head is showing, we're gonna cover it with some hair coloured wool.
Grab a little wisp of the hair coloured roving.
Lay it along the back of the head between the hat and the body.
Felt it into place.
Don't worry too much about how you felt down the pieces around the front of the face. Those are going to be covered up in the next step.

Step 8: The All Important Beard

Beard time!
Grab a wisp of the beard coloured roving.
Fold it in half so that it looks like the picture above.
Felt the top part along the face and under the nose.
Repeat to add on another layer or two.
Felt the beard down into place. I like to give it a little curl at the end, but that's up to you!