Fuseki: Fuseki is more commonly known as the opening. Many players often underestimate the value of a good opening, as this is what sets the tone for the rest of the game. It is also where you have the most options to manipulate the game around your style of play. Much of the time players will play for the biggest territory possible, starting in the corners and reaching to the sides and then proceeding to come up with a strategy to remove and gain more territory than the opponent. Some strategies including setting up huge possible territories that entice invasion or keeping groups unstable to make things complicated. You are free to experiment!
Of course, I am no pro so the below example is certainly not the best way to go about it, but it’s all in the learning. What is important in Fuseki is the potential of groups, territory, attacking, defending, and everything that goes with it.
Joseki: Joseki are patterns for proper consecutive plays that have been devised over the centuries and tested by the best go players and used prominently by all go players throughout. The thing with a joseki is that like any pattern, it can work well within a scenario, but it can also work poorly. The whole board must be taken into account when choosing a joseki to play or where and how to deviate from it. It is very useful to study joseki (see Josekipedia) so as to recognize patterns. It is more useful to understand why joseki are joseki and to be able to deviate properly or punish improper plays.
Below are some basic corner joseki variations. There are many more continuations and other ways to respond, but this is just to give the general idea.
Influence and Moyo: Each stone has a field of presence that exerts itself across the entire board. As the opening progresses, just take a moment to visualize how all the stones on the board give off a strength to their surroundings and in relation to each other. The presence is called influence. Influence grows with strength of multiple stones, which can become much more noticeable when entire walls of stones are built. The primary rule of large amounts of influence is to play away from them, whether it is yours or your opponent’s. If you play near a large wall of the opponent, you can be easily attacked. If you play near a large wall of yours, it becomes inefficient and hard to use. A moyo is what can be a called a framework of stones (potential territory). A moyo uses influence in such a way as to threaten to make a huge amount of territory if the opponent neglects to respond.
Reduction and Invasion: Viable responses to moyos, or potential territories in general, if you are behind are either reduction or invasion. Reducing means limiting the size of your opponent’s territory from the outside by playing to threaten to break into his or her territory. Invading is playing directly inside the potential territory and trying to live a group inside. Invading is often considered risky but more rewarding and reducing is much less risky but not quite so rewarding.
Attacking: This is what influence, moyos, and strength are all about. When you have surrounded a weak group, it is important to attack it in such a way as to gain profit by it even if you cannot kill it. Properly attacking involves playing farther away from a group in order to surround it when it tries to run. It is also important to use your walls and influence in the course of an attack to get the most use out of them.
Sente and Gote: Sente is known as initiative, having the freedom to play first after a local situation has been decided, or just being able to choose where to play next. A sente move is a move that the opponent must respond to. Gote is exactly the opposite, which is having to respond to a move or losing initiative. Being able to operate your strategy while maintaining sente (getting the first play in sequences) is the mark of an experienced go player. However, there are many times throughout games that playing gote is proper and necessary, such as backing up glaring weaknesses. This subject is often considered the most underestimated complex subject in the game.