MULTIPLAYER GENERAL TIPS
Diced Tomatoes is a simple dice drafting game with a bit of strategy/tactics. The main thing to know if that the dice placed on the tomato token becomes the score thus it is important to start your tomato vine with the highest number possible. If you roll a low number you should "gift" it to your opponents. This locks them into scoring a low number if the vine is completed.
Use the "rotten' (black) dice strategically.
They can be used to lower opponent's score value but also to help you clear unwanted low-scoring vines.
Say, your opponent placed dice with value of 1 on your tomato. There are two ways to prevent yourself from scoring that 1 point - 1. use karma to clear the entire vine, 2. try to roll a black dice match to this vine (like 1 or 2) which will clear the vine at the end of your turn.
Picking 3 black dice or 3 gold dice on the first turn of the game IS NOT A GOOD IDEA - those dice cannot be placed on the tomato token so you will have to pass them all to the next player.
Another tactic you can employ is to drain the dice pool in order to finish the game prematurely. The game ends immediately when a player starts the game without any dice in the Bushel. So if you either place dice without generating a score or pass dice to the next player when there are no dice in the Bushel you can trigger the end of game.
Don't be afraid to complete opponent's tomato vines
Completing opponent's vines earns you karma points which give you some abilities to change things on your turn. Use black dice to complete opponent's vines, especially if you can lower their score by more than 1 point - remember, the karma you score is based on the seed dice (the dice placed on the tomato token) and not the score they get. So if you finish opponent's vine with a seed dice 5 but with 3 black dice attached to it they only score 2 points while you score 3 karma (based on 5 seed points).
SINGLE PLAYER TIPS
The point of the single player mode is to train yourself how you can and when you should modify the dice by using the Karma, black dice and gold dice (if you choose the Sunny Gold Hybrid variant).
Single player mode can teach you the role of the "rotten" dice. You can win the game by sheer luck but if the dice are not on your side you can use the black dice to change the situation to your benefit. Remember that just because you placed a 3 on the tomato token doesn't mean that you have to score that number. You can add 2 black dice to lower that score to 1 for example.
Similarly you can use the gold/yellow dice (part of the Sunny Gold Hybrid) to raise the score of the vine or to cancel out any black dice already on the vine. Note that if you raise the score too high (over 6 points) the vine will score nothing when completed.
Don't be too quick to use hearts at the beginning of the game. You will most likely need them towards the end. You earn hearts every time you score even if your score is negative.
Sometimes it is a good idea to prevent a dice from being placed if you have the hearts to change its value. When you pass the dice you will roll a larger set the next turn which might give you more options to choose from.