Semicolons are not hard to use; however, they can be risky in the wrong hands. We are more comfortable with commas because they are cheap, easy to deploy and don't call much attention to themselves whether present or missing; semicolons, on the other hand, tend to call a halt to everything and say, "look at me!" Why? Because they show a good author paying attention to a sentence, its structure and rhythm, its balance and weight--unless they show that a poseur has turned up garishly dressed for the wrong party.
The rule behind a semicolon is simple: use it to join two independent clauses into a single sentence. What the hell is an independent clause? A thing that could be a sentence all by itself if it wanted to. For example, the present sentence is an independent clause. So is this one. But the collection of words presented as the last sentence of the first paragraph above is not--that pesky because turned it into a fragment, and then that nervy unless kicked in for good measure. There's another sentence fragment skulking in this paragraph, by the way, and skulk it should. A good fragment tries to pass unnoticed: “no one here but us sentences.” In any case, the payoff for competent semicolon use is large because it shows that you are in control of your sentences, that your sentences know how to behave in public; the risk of casual use, however, can also be huge because there is little worse than a loud, obnoxiously dressed sentence running around an otherwise refined gathering.
Words like however often cause a need for semicolons to arise; however, not every however requires a semicolon. It's the same rule as above: use a semicolon to combine two sentences into one. If you use it well, it will create a neat order within a commonly sought pattern; however, the one does not always cause the other. You would not use a semicolon in this sentence, however tempted you might be. That's because you aren't combining two sentences into one anymore.
The common pattern is sentence; however, sentence all dressed up in cocktail party elegance and ready for polite conversation. If you do it right, everyone is impressed and happy with your savoir faire; however, if you mess the pattern up, you've shown up to the party in your madras shorts and will occasion behind-the-hands murmuring. Your scarf, it was not apricot. And, for the sake of Thoth, never follow however with a semicolon; that, like flip-flops at the cotillion, will cause guffaws and pointing because you have stumbled and we have all seen why. Wrong shoes for dancing, convention boorishly ignored, clouds indeed in your coffee.
However, like consequently and otherwise, is a conjunctive adverb, so while it doesn't have the power to glue two sentences together, it does point out how ideas relate to each other. That's why you often need the semicolon for sentence-strength adhesion; however, don't confuse it with words like although and because. They are conjunctions--transmogrifying conjunctions--which demote sentences into phrases, as we saw in the first paragraph, and thus don't occasion the sentence-joining power of a semicolon. As a result, you would not write this sentence; although, your speech patterns may tempt you to do so. If you did that, you'd get more pointing and guffaws. Until you get the hang of it (by writing!), the best way to sort through what words are conjunctive adverbs and what words are subordinating conjunctions is to look at lists, which you can find by, well, clicking those links.
If you've got a complicated list on your hands, say a series of actions, for example, then semicolons can help you impose some order on things: I made my coffee; I marveled at the wonder of punctuation marks; I was writing my blog entry; I saw once again how it's the little things that keep our prose running smoothly. Or you might have a list of lists, which can get really complicated; in that case, semicolons can help you keep things sorted.
Here are some things you need to write well: inspiration, ideas, dedication; a pen and paper, or a keyboard and screen; words, sentences, punctuation and paragraphs--and at least one reader (yourself, perhaps?).
That list of lists would have been chaotic without the semicolon reigning things in. It compels everyone in the sentence to stop gadding about immediately, sit down and stay put so we can get on with figuring things out in an orderly fashion.
Although semicolons do sometimes play an important role in list-making, they do not play any role at all introducing lists--use a colon for that (colons say, "look ahead!" semicolons say, "you! stop there!"). An ordinary list might consist of three things: a mouse, a cat and a dog. You can see that the chase is on, all set in motion by an introductory colon. Watch what happens if we introduce the same list with a semicolon; the cat, the dog and the mouse. See? They are all happily asleep on the fireplace rug, ignoring each other and unroused by the failed sentence; perhaps one of them twitched an ear at the infelicity.
Sometimes writers rebel against the established conventions of editing clear prose; the really good ones get away with it. It is inadvisable to try this with semicolons, however, because they wave their hands, calling out; "hey; look at me! I'm breaking the rules!" That's not slick at all; just indicates you don't know what you're doing. Semicolons are not the poor man's colon. Do not use them to introduce; lists, complicated sentences, anything. Nothing says; "I don't know what I'm doing"; more than a misapplied semicolon. Like a Hummer at the wilderness trailhead, it tells all the hikers to be wary of the oaf doubtless crashing through the woodland preserve. If you must, if it improves things, break rules with commas, they are much subtler, they let you get away with more, they work on the sly, hardly noticeable until someone exclaims, "Look at what he just got away with!" Well done, prosician!
So, use a semi-colon to combine two sentences into one; you do it like that. It is a good idea if the sentences are closely related; otherwise, they probably need a stronger separator, like a period. They can be useful to indicate relationships; examples or cause-and-effect might provide occasions thus: "The weather was cold and rainy; I did not want to ride my bicycle that day." Use them judiciously, for they have impact; they force a halt; they impose a rhythm. You don't want to overuse them; they can get tedious.
As with any powerful tool, use semicolons carefully and sparingly. They can balance a ponderous sentence; they can tame an unruly thought. They can reign in feral prose, but they don't do it subtly; instead, they impose order, rhythm, cadence. Used well, they help readers sort through your ideas, uncomplicating your thoughts. Used poorly; you've got an ugly cement wall running through the middle of your beautiful landscape.