Many volumes have been written on Go strategy. This page will not get into much depth, but will address the concerns of the beginner. The most important thing to understand is that you want to consolidate your gains in territory. Your stones are perfectly secure from surrounding when they contain within them two separate areas of liberties. The smallest possible secure area is shown in our example. Notice that any incursion by black would necessarily be a suicide.
Many new players try to take and defend the middle area of the board. This can be a mistake because it does not take advantage of the defensive area known as the edge of the board. Note in our example how black cannot get behind white lines. White has more efficiently walled off territory than he might otherwise have. Yet a player must be careful not to play too close to the edge, because while it takes away an opponent's options, it also takes away a player's liberties. It is best to operate about two points from the edge. Most Go boards will actually highlight these points.
Think of these highlighted points as places around which to secure territory. If your opponent leaves these areas open behind his lines, it can also become a point of attack.
Remember that it is not the object of the game to take away and destroy all the opponent's territory, a player needs only one more point than his opponent to secure victory. For this reason a player should work to simply conquer a bit more than half the board. Risky and wild play will generally only work to a player's disadvantage. The best way to say it is, "don't be greedy". Let your opponent consolidate, if you can consolidate more.
Broadly, as in any strategy game, it is often productive to try to view the board from your opponent's perspective. If you were him, what would you fear the most? This is an especially helpful technique when offensive play is called for. A great book for beginners is Lessons in the Fundementals of Go, by Kageyama Toshiro.
Perhaps the best advice for the new go player is to learn the old fashioned way, by doing. Play, Play, Play.