I noticed that this topic is not used too much, especially not right now, and I realized that it could be used a serious teaching tool for younger players. So, I at least, will be making contributions to this topic based off my own experiences and knowledge.
Splitting
Summary: So, first off is a very simple concept which most players I have met have referred to as splitting. Essentially, it is when you use one unit to separate an opponent into two sets of connected regions for the purpose of limiting the units they can place on the next turn.
Applications: When a large opponent has one or two regions somewhere near their center. Splitting is one of the best ways of quickly evening out a game.
Offense: If you are close enough to your opponent's center, and have a decent attacking unit or two, use them to try and take that center for yourself. If the split is successful, you should notice that the contiguous region count beside their name on the right side of the screen has dropped considerably. This is because you have not only taken the one or two regions you conquered, but also completely cut away what should be quite a large chunk of their color.
If you are playing manual mode (in other words, if you have a choice of where to place your reinforcements), you should make sure that the new blockade is now well fortified and, if possible, protected with shields (defense boosts). If your opponent reconnects, don't be too bothered, just keep splitting them.
Counter: If you have a thin center area, as described above, and you have an opponent who is or could soon be capable of splitting you, you should take action there if you seek to keep your advantage. Two things should be done: First, make sure to keep strong units and defense boosts (if possible) in the 'weak' area. Secondly, work to expand your control into white areas or your opponents around your center, as to make it much harder to split you.
PS, I also have a question for anyone who thinks writing these things are actually a good use of my time for the future: Do you think I should continue to post them as, like, a daily lesson type thing here, or should a new topic be made so that I can edit and add everything I post and that other people post into a comprehensible list? That way people who actually want to learn (or ridicule me) can get everything I've said in one place.