
This opening move means that Black does not mind losing the corner and that he will still play for territory, as this move is on the 3rd line.

Komoku: this is standard opening move for territory and helps control the top side from the upper right corner.

Hoshi plays are for influence, so the next best move is to play at either D10 or K16. If White approaches at either C14 or F17, standard reply is at either of these points to make a corner enclosure. Playing a 1-point jump (
ikken-tobi) on the 4th line is OK if you already have a stone at either C10 or K17. Having a stone on one of these two points is good since you can make a 2-point jump on the third line if White invades, mainly by playing on the 3rd line. The high-low balance along the side is desirable, since having all stones on the 4th line means you play mainly for influence and that you will not be getting much corner or side territory. Conversely, having all your stones on the 3rd line means the opponent will play on 4th or 5th line to keep you out of the center, so from a 3rd-line stone that is part of a group of 3rd line stones an
ikken tobi to the 5th line is often played to prevent this.

After this move I would play on D10 to reduce the potential of this White stone or on K16 to deny the side extension to White from


The sequence up to

is OK, but I would have played

on Q9 to help out

Otherwise, I would have let White have the top right corner and instead play this move at L17 to reduce the potential of White's upper right corner. Do come back soon and reinforce with a move at G16, as the area is very open and vulnerable to invasion. If an invasion does occur, though, reinforce your L17 stone as this would be the weaker stone.

would be better at K4 to increase the influence of Black's lower right side wall.
I recommend avoiding fights if possible during the opening, as your opponent can gain benefit from them. By

, White has tremendous outward influence and Black's stones in the center left still do not have any eyes, with a somewhat strong White corner group right below. As well, avoid trying to deny your opponent all territory. You could have come out well in the opening if you simply developed your global position and let White do the same with his global position while paying attention to the strategic balance of power on the board. I used to do this and I often lost games if my opponent knew how to respond to my moves. Recently I adopted the attitude of letting White (or Black) have what he wants so I can win by 1 point, rather than trying to win by 20 points.
To improve your opening skills, I recommend replaying pro games for the first 100 moves. (I prefer that you replay each one from start to finish, but if your want to know about opening moves the first 100 moves provide more than enough information.) Yilun Yang 7p's
The Fundamental Principles of Go is a good book explaining opening theory. It can be purchased in North America from Slate & Shell Publishing.
Also, it is in the opening and middle game that one gets to see what kind of playing style a player prefers. Some like to get territory early and so they will play komoku first. Others like to play for influence and so they will play on star points first. There are those that play for territory and like to fight, and there are those that play for territory and don't like to fight unless necessary. There are those that like to play for influence and like to fight, and there are those that like to play for influence, but don't like to fight unless necessary.
I notice that Black was playing for influence. This is known as a moyo style game and in this kind of game you play opening moves on 4th line, prepare mainly to attack your opponent's groups from the center by making a big moyo, and attack your opponent's weak groups to make territory as you fight. Usually your opponent will invade your moyo and you get points by attacking the invading group. Territory is generated as a result of the attack.
When attacking,
attack from weak towards strong. In moyo style play this means attacking your opponent from the center towards your strong groups on the corner and sides of the board.
A basic summary of the purpose of the first few opening moves.
A play on 4-4 or any of the other corner star points is for influence, since the corner is open and can be invaded. Ideally you should extend to a side star point. If your first play is on 4-4 and all the corners are taken , play next on 10-4 or 4-10 is ideal. If your star point stone faces a komoku corner enclosure, extending towards that enclosure to, say, 3-11 or 11-3 will reduce its potential.
If you play on 5-3, your next move should be at 3-4 to make a secure corner enclosure. Then the next move should be to . This is a territory-oriented series of moves, so avoid trying to make a moyo and play high (normally 5th line play) only to reduce the potential of your opponent's moyo or center territory. If you play on 3-4 first, play next on either 5-3 or 5-4 to make a secure corner enclosure. If you choose to play 5-4, as this stone is on the 4th line extensions from it should be on the 4th line as well.
If you play on 4-3, you can develop for influence along the 4th line, but only for territory along the 3rd line. Normally, komoku plays are followed by making an enclosure, then extending along the side, usually from the "low" stone (komoku). In the days before komi, a corner was worth a lot, so 1-point keima approaches against komoku were common. In modern play this kind of approach against komoku is often played to prevent the formation of a corner enclosure, which is still very valuable, and as a precursor to joseki.