[Base game]
The biggest part of the game revolves around hindering your opponents from making cities (or roads), and preventing them from stealing yours.
Since the base game has a pretty restricted set of tiles, blocking enemy meeples is quite easy.
A city with only one meeple is vulnerable to being stolen, but one with several meeples is vulnerable to getting blocked. If your city becomes impossible to complete, your meeples will be imprisoned there, which is a big handicap.
For these reasons, avoid building giant cities, and go for several small ones instead, and make sure they aren't interesting to attack by your opponents.
Also, try to avoid using too many meeples at once (e.g. building 3 different cities, you should focus on finishing cities/roads).
In fact, you should try to always keep at least 1 meeple in your hand until the last few tiles.
If playing on a smaller device, be careful where you place your meeple so you don’t “miss” the spot you actually wanted to place it. Try expanding your screen first before making a move.
[Traders & Builders]
Make sure you use the builder as early and often as you can. Avoid using it only if it is vulnerable to being trapped by your opponent.
Focus on building cities as often as possible. Roads are already quite weak in the base game, but with extensions, and the "resources" available in cities, they are even less fruitful.
For the same reason, it's not always worth putting a meeple on an abbey/monastery : will you really be able to get it back ? Is the risk worth only 7 or 8 points ?
Don't waste your big meeple on fields (except at the very end, of course). It's particularly precious, for both attacking and defending cities.
Also, obviously it's very important that your big meeple doesn't get trapped. It's way more inconvenient than losing a regular one.