Transitioning to the Net  

Look at the court as being divided into three areas: the baseline, no man's land and the net area. (see graphic) 
- The baseline is where the point starts. But if your intention is to move up to the net behind the serve, then the baseline is like your starting place - Ready! (toss)… Set! (hit)… Go! (move towards the net).
- No Man's Land is the space between about one foot inside the service line and about a foot inside the baseline (see graphic). It's called that because this is where the player should not be caught playing too often, or at least the player should not wait for the ball in this area. I like to call it a "transition" area - hit the ball and move either forward (to the net) or back (to the baseline). 
- The net area is the space between the net and about a foot inside the service line. This is where you want to get to in order to play aggressive tennis. The closer to the net the better, but you do have to consider covering the lobs too. 

The transition to the net can be done either following the serve, the return of serve, moving up on a short ball during the rally or lobbing the opposing net player.

1. Serve and Volley
a). Your transition to the net, to be a successful one, has to start with a "smart" serve… It has to be slower (so you have more time to move up) and lower (so that the returner hits the ball up). 
Slice serves are the better option considering that the ball stays low (forcing the returner to hit up) and the spin also slows down the ball in the air giving the server more time to move closer to the net.
I suggest that you avoid topspin serves when intending to charge the net because they kick high and make it easier for the returner to hit down at the approaching player's feet. 
Also the placement of the serve should be as close as possible to the center line. Hitting the ball wide puts both the net player and approaching server in a delicate position (by opening the court in all directions for the returner). But don't do it all the time, vary the serve placement to keep the opponents honest. (see Serve Placement)
As you deliver the serve, your forward movement has to begin right away. Toss the ball more in front so that you get some forward momentum. 
b). Moving through No Man's Land is the most difficult part. Your job is to move up towards the net right after the ball has left your racquet. The next shot is frequently a low volley or half volley since the returner will try to put the ball at your feet. So the first steps after the serve is delivered are going to be running steps. Then, as the returner is just about to hit the ball back, you should shorten your strides (stutter steps) and eventually get into a split step. The split step is a small hop just before the opponent contacts the ball. It helps the approaching player to gain his balance and be ready to push off in the direction of the incoming ball. 
This split step, depending on the speed you delivered the serve, should occur somewhere around the service line (either inside or behind it).
A fast serve allows you to make just a few steps toward the net, a slower serve gives you more time to get inside of the service line, at least. That's why, in doubles you will not see very hard first serves for the simple reason that the server needs more time to get closer to the net. 
So considering that the first volley (or half-volley) is done around the service line, this should be treated as an approach shot. Since this is a low one, all you want to do is keep the ball away from the net player and direct it deep toward the back player. Keep the ball away from the opposing up player but at the same time you should try to make it land not very wide either. I know, it is a difficult task to do… 
Execution: right after the serve is delivered, make sure you have the grip on the racquet ready for a low volley. Keep the racquet face in front of the incoming ball and get your body low (from your knees). Catch the ball on the racquet face and push it gently without any backswing or follow-through. An important role in executing the low volley is to get low - lower the eyes close to the ball. 
c). Once the first volley (or half-volley) has been successfully delivered deep to the opposing baseline player, your next job is to move beyond the service line and position at the net. Split step and get ready for a higher volley. Hands hold the racquet out in front, relaxed. 

2. Serve Return and Approach
To move up to the net on the serve return you will have to take the ball on the rise. Position yourself inside the baseline in order to do so. Use a very short backswing and meet the ball out in front then let the momentum carry you forward. 
You also have to adjust the return placement according to what the server's intention is - stay back or charge the net. 
If the server decides to stay back, then attack the ball and push it deep, floating and cross-court. Or you can chip-and-charge: hit a drop shot on the baseline player's side. 
If the server comes up to the net, return down to his feet, making the ball land in the service line area. Your serve return should be made with three goals in mind: keep the ball away from the opposing up player, give you time to move up (slow) and make the server hit the ball up (low). 

3. Moving up on a Short Ball
This is a running shot that gives you forward momentum going into it. 
Same as previous shot (serve return and approach), your goals are: keep it away from the opposing up player, send it deep and low and also make it float (underpin) so you have more time to get up to the net. 
As you move up, stay behind the path of the ball in order to close out your opponent's possible angles. 
Placement wise, you are looking to either send the ball deep toward the opposing back player or drop shot away from the opposing up player. Avoid hitting the ball to the mid court because this gives the opposing back player a chance to attack it aggressively back to you. 

4. Lob Approach
This is an exciting shot to make considering that it gets the opposing team switching positions and gives you plenty of time to move up to the net (if the lob is successful). 
Your lob shot should be aimed over the net player that is in front of you, and deep to the baseline. Make sure that you wait to see that it clears the opposing net player before you move up. Otherwise you can find yourself in front of a cannon ball aimed at you. 
If the lob is successfully executed, as you move up to the net, expect to get another lob back as a reply. Communicate with your partner early about who is going to take the overhead (while the ball is coming back to your court). Consider that the player whose forehand is closer to the center to take the overhead aimed between the two of you. 
Execution: The lob can be done with topspin when you are set up and have plenty of time to get under the ball, or flat and under-spin when you just want to block a fast incoming shot.