Think twice before moving, thrice after losing. Do not be discouraged after a loss - reflect and experiment: enjoy the game!
Opening
For the opening, there are a vast amount of possibilities and variations. An old saying is that you should move one of your chariots by your third move, or else it will be too late. Do not attempt to go deep into your opponent's half too early using just one or two pieces; very likely your pieces will be trapped and wasted. Combine the power of your pieces to introduce threats to your opponent. Also analyze whether your opponent is aggressive or defensive, and adapt to their games.
Development
Capturing your opponent's piece may not be the best move. For example, capturing your opponent's soldier on the outermost line (1 or 9) before it has crossed the river using your own horse may not be a wise decision. Your opponent's piece did not pose any significant threat to you, and you are limiting the options of your own attacking piece, especially the horse, which is prone to being 'hobbled'. This buys your opponent time to create powerful moves, so a general tip is not to capture a soldier only for the sake of capturing it. Conversely, do not be afraid of losing pieces - this is a must throughout the game process.
Another tip is to not always run away from your opponent's capture attempt. Escaping your opponent's capture attempt means that you are giving up your own territory to your opponent, which often results in your opponent having good control of the board. A better method to counteract your opponent's attempt of capture is to guard your piece with another piece. For example, if your cannon is under direct threat from your opponent's chariot, you may choose to guard it with your horse, or even your soldier if applicable. Your opponent probably won't exchange a chariot for a cannon. Here are the estimated values of attacking pieces in general (unofficial, for your reference only): Chariot (9), Cannon (4-5), Horse (4-5), Soldier (1 before crossing river). That is, a chariot is worth roughly two cannons or two horses. Exchanging pieces is also a technique to master. Apart from the values of each piece, also consider the positions of the pieces. For example, a soldier before and after crossing the river have significant power differences. Advanced players will even consider giving up pieces in order to get faster control of the board, but this should be calculated very carefully and thoroughly before execution, else you will be giving up your match.
Check
To checkmate, plan your attack well. It is almost impossible to checkmate with only one attacking piece. Therefore, do not try to check using one single attacking piece - there is no actual threat, your opponent can easily dodge or block. Instead, you may have to use three or more pieces to check continuously to win. Another 'mistake' that beginners make is to exchange one of your opponent's defending pieces (elephant or advisor) using an attacking piece, thinking to destroy opponent's defense. However this is unlikely to be effective, since you moved quite a few moves in order to exchange for a piece that seldom moves, meaning that you wasted a few moves. Moreover, your opponent can make use of their attacking pieces for defense. However, it could be a good move if you can capture your opponent's defending pieces without an exchange, although this is not necessary for a win.
In fact, a lot of wins are created by the advisors limiting the possible moves of the General, therefore it is not a must to start your attack only after no opposing defense pieces are left.
Defense
To defend a check, the most easy way is to dodge or block, if the opponent piece is impossible to capture. Nonetheless, it is usually better to avoid being checked in the first place by anticipating where your opponent is going to place his piece to check and guard that point before a check actually happens.
Another way to defend is by aggressive attacking - leaving your opponent no time to attack - but in most cases, remember to keep a few attacking pieces behind since they should be participating in defense too. It is not enough to defend by using just elephants and advisors. Another fact is that although some pieces - such as the Cannon - can move from one end of the board to the other in one move, they are easily blocked too, both by own or opposing pieces. This is another reason to not push all of your attacking pieces forward while not being able to win, leaving your opponent a good chance to counterattack. For example, one Chariot can stay in your own half to defend, while keeping the potential to go out to assist attacking in just one move.
Overall
Xiangqi is a very strategic game involving virtually no luck. The only way to improve is to play more with different players and experiment more. Every move counts, so plan your moves well ahead, and anticipate what responses your opponent is going to give. Try to understand your opponent's intention by their moves, so as to make a correct judgement and eventually win the game.