Go is more about surrounding territory (empty space) than capturing your opponent's pieces.
Territory is easiest to surround near the corners (on two sides) then near the edges (on three sides) and lastly in the center.
At the start of the game, space your pieces out. Only fill in your fence-lines when your opponent starts to intrude
Do not play unsupported stones right next to your opponent's stones when attacking. They will tend to get swallowed and GnuGo is very good at that. It is often better to attack indirectly.
To avoid capture, a group of stones must have two “eyes” or be able to make them if attacked. “Eyes” are disconnected spaces. Think of a doughnut with two holes. Your opponent can surround the outside, but cannot fill both holes at once.
On the 19x19 board there are typically several territories being created, attacked or defended. You have to fight several battles simultaneously. The strategy involves evaluating the strengths and weaknesses in various areas and allocating your moves between them. Is it better to attack there or defend here?
As the board fills up and the end-game approaches, it becomes important to play closer up, nibbling at your opponent's fences or reinforcing your own. Small mistakes and omissions can become very costly.