Tic-tac-toe is a game of perfect information, so best play always draws. What changes on bigger boards, gomoku mistakes and principles you can use.
Tic-tac-toe, gomoku and connect four all show the whole board, involve no chance, and have finitely many moves. Games meeting those conditions have a theoretically determined outcome. With best play from both sides, either the first player wins, the second player wins, or it is a draw. Which one differs by game. Mathematicians call these combinatorial games; with no luck involved, the result is decided entirely by the players' choices.
The board is small enough to examine every possibility, and the conclusion is that flawless play from both sides ends in a draw. Winning at tic-tac-toe therefore means the opponent played something less than best somewhere. It is also why you rarely beat a computer at it. For beginners, taking the centre or a corner first is the starting point for avoiding mistakes.
Connect four has also been fully analysed and is known to be a first-player win with best play. On larger boards such as gomoku, the first player's advantage is so strong that competitive rules restrict the opening placements to rebalance it. Rules that look complicated usually exist to correct exactly this kind of imbalance. Since a single rule change can flip who has the advantage, agree on the rules first when playing someone new.
Chess and go satisfy the same conditions, so their results are determined in theory. The number of possibilities is simply unmanageable, so the answer cannot be obtained. A solution existing and a solution being computable are entirely different problems, which is why these games remain interesting. That is why even strong players rely heavily on a feel for good and bad shapes built from experience rather than calculating every move.
There are principles that work without memorising a complete solution: block the square where the opponent wins next, and build a shape where you threaten to win in two directions at once. Faced with two simultaneous threats, the opponent can only block one. Most games turn on who builds that shape first. This double threat works on the same principle from tic-tac-toe to gomoku, so a feel developed in one game carries straight over to the others.
New gomoku players often concentrate on linking their own stones and miss the opponent's threats. When the opponent makes an open three — open at both ends — it becomes an unstoppable open four on the next move, so an open three must be blocked as soon as you see it. A four closed at one end, by contrast, needs only one block. Knowing this distinction alone cuts down on silly losses enormously.
Much of the difference in strength comes from what you check before playing. Building the habit of running the same checks every move cuts mistakes sharply without any complex calculation. First see whether you can win right now, then whether the opponent can win next move, and only then choose a move that builds your shape. Swap that order and you miss wins or fail to stop losses.
A computer opponent never tires and punishes mistakes precisely, which makes it a good sparring partner. Start at an easy level to absorb winning patterns, and move up once wins become common. For a lost game, tracing the last few moves backwards usually reveals the cause in one or two moves. Aiming never to repeat the same mistake three times leads to steady progress.