How can I link my paragraphs together effectively in an essay?

This is something that comes up frequently with students: how can I effectively tie my arguments together in an essay, so that the flow of the writing makes logical sense. The answer is - with a jigsaw!
This usually works better with a diagram (not that my drawing skills are up to scratch), but it is useful to think of your essay as a long vertical jigsaw puzzle, one piece wide. Each piece (or paragraph) needs to connect to the piece (or paragraph) above and below. Each paragraph should start with a line which refers back to the previous point you were making, and then close on a line which clearly moves towards the next point you want to make. This ensures that your essay is coherent, with a good flow for your reader/examiner. This also means that the core argument of your essay is supported by a strong structure.
But what if your points don't link at all? Well, this is a sign that you haven't structured your essay properly, or are trying to shoehorn really disparate points into the same argument. Of course there are times that linking points together can be a bit of a stretch, but they should never be so far apart in content that reading them side by side feels like a total gear change. Sometimes you might need to look at your other points and paragraphs, and consider which make the most logical sense to put next to one another - it can take a bit of creativity to blend your points in a coherent manner. Other times, you may need to look at whether an argument belongs in an essay at all - and this is just as important a lesson to learn.