Tiddlywinks is a game with a strong strategic component. Novice players may wish to consider the following basic advice.
The colours always play in alphabetical order. If you have the chance to squop either of your opponents, you probably want to squop the one who'll play next. Your partner will then have a chance to attack the other opponent. Another reason that it can be better to squop the wink that plays after (rather than before) you is that your wink may be knocked off the squop by an attacking opponent. If you play immediately before the colour you're squopping, you'll have a chance to climb back on before the wink can be moved away.
If you have a large number of winks near each other, they can defend each other. This is especially true if both friendly colours occupy the area - any opposing wink that lands in the area can then be attacked by two winks before it can be played again. Winks that are spread-out, however individually well-positioned, can be captured without there being an easy opportunity to free them again. Many games start by moving the edges of areas around, without ever placing a wink where it is undefended (this is called an "Inglis game", named after a player who particularly advocates the strategy).
Capturing a single wink on its own gets you a table point and ties down an opponent, but it also removes the mobility of one you your winks. Attacking a singleton is dangerous because they are often highly mobile and can be played onto the attacker. Winks which are squopping two or more opponents are far more valuable, leaving winks free to defend.
When your opponent has six winks sitting next to the pot, it is often too late to try to squop him. Unless you have credible counter-pot (so that your opponent doesn't dare to miss), it's usually better to commit one colour to being squopped in order to stop that wink being potted.
Bringing the winks near to the pot in a way which threatens a pot-out is often enough to give you a big advantage: even without needing to pot out, your opponents will have to throw winks into your area in order to stop you, so you will have a strong start to a squopping game.
Nobody gets every shot they try. However, it's possible to consider the way that a shot might go wrong - it's usually better to spend time thinking about this than to plan lots of shots ahead, assuming that you and your opponent will get everything. It's usually not worth trying a hero squop if it will mean your opponent can easily capture you.
If an opponent is threatening to pot out and has three winks near each other and one separated, it can be better to attack the three. If the opponent wants to pot, he won't want to squop you, so being in his area is relatively harmless. If you miss a solitary wink, the opponent will have a change to move it before you can attack (even if a pot attempt misses); if you land among several, all but one have to be potted in a single turn, else you'll have an easy shot on the remaining winks.
It's often valuable to tie up one colour of your opponents - however many winks the other colour has, they can only be played one at a time (unless they're being potted). If you have two colours free and able to play for every shot of your opponents, you have a strong advantage. This advantage is doubled if one of your opponents is stronger than the other, and you have the opportunity to gang up on him.
Much more information about tiddlywinks strategy can be found on the ETwA (English Tiddlywinks Association) web site and in Winking World magazine.