Black 4,4 (hoshi, star) is a fast and center oriented move, very popular in recent professional Go. The 4,4 move leads to simple and easy to understand joseki variations which also makes it a popular move amongst amateurs.

Black's continuations

If black wants to develop the 4,4 stone he can play large scale with A or tight with B or C.

White's continuations

White usually approaches the hoshi stone with C. When approaching from the side is not interesting white can take the corner by invading at D.

White approaches with 2 and black 3 prevents that white attacks the corner from two sides (with either 3 or A). If white wants to settle a group immediately he will slide with 4 and extend with 6.

When the lower side of the board is interesting for black to develop he will answer white 2 with the higher move at 3. Since the corner is still open for invasion (at A) white usually will not slide to B (as in the previous diagram) but play any of the points C to settle the situation on the left side of the board.

This is a typical fast-paced development around the hoshi stone.

When the left side is interesting for black (the upper-left corner is black for example) he can choose to attack white from that direction with black 3. White will usually settle his stone by invading the corner and take some territory in the process.

When black has a stone around A black can build the wall in the other direction with 5 as in this diagram. Please note that white ends up with sente this time.

One of the nice things about Go is that things are never that simple. For example, when black plays 3 hoping that white will invade the corner and black can build a wall as in the previous diagram white can frustrate black's plans by playing double-kakari with 4. Black 5 is the natural move and white manages to settle a group along the lower side of the board.

By the way, this is one of the more complicated 4,4 joseki. You don't need to study this joseki if you feel you're not ready yet.

For balance with the upper-left position black can choose the higher pincer of 3 as well. As with the low pincer white can play simple and invade the corner leading to exactly the same sequence as before.

When white doesn't like that black closes off the left side as in the previous diagram he can play as in this variation. White settles his group by sliding twice with 6 and 8.

This variation shows that white has more options compared to the variation in diagram 4,4-31. That's why the one-point low pincer (3 at A) is gaining popularity recently.

As with the one-point low pincer it is possible for white to decide to settle along the lower part of the board by playing double-kakari with 4. Black 5 is a natural response and the variation proceeds almost identical as in diagram 4,4-33. White settles along the bottom and black becomes strong on the left side. This variation is reasonable for white since he ends up with sente.

It is possible for black to ignore (for all kinds of legitimate reasons) white's approach move at 2. The natural continuation for white is to play another attack on the corner with 4. Black 5 is essential: split 2 and 4. The moves proceed naturally up to 15. Black is thick and white is settled along the bottom.

Black can also look forward to a nice kikashi at either A (white will answer B) or C (white will connect). Which kikashi is best can be decided at an appropriate moment later on in the game.