Since not a lot of Agents or Casting Directors have the time or are even interested in coming along to shows to see actors perform for possible representation/casting, a showreel is a great way for them to see you perform without the hassle of travelling to shows.
For the beginner Actors, a showreel is basically your Visual CV. A 5 minute (roughly) collection of your previous screen acting work, which will give Agents and Directors a taster of what you're capable of as an actor.
So the best way to get a good showreel put together would be to pick out a few scenes that you have been in, which show you off as an actor. Make sure the scenes are contrasting (i.e. comedic/dramatic, difference in the mood or style of the scenes etc), this will show that you are not limited to a certain type of acting (i.e. you can only do comedy etc). You also want to make sure that you pick the best quality scenes, as a professionally shot and edited scene will make a better impression than a bad quality scene with bad camera work.
To get your showreel made you'll want to get in contact with Independent Production Companies, or companies that specialise primarily in making Actors' Showreels. You can find these by doing a simple search through the internet, by word of mouth from other actors, or even social network sites (you can find filmmaker and actor groups on facebook and find people to help make your showreel there). But if you can't afford to pay for companies to make your showreel, if you have any friends, or know anyone who is studying Filmmaking or Media at college/university you could get in touch with them and see if they would make your showreel for you, as they might be able to do it for free/a low price.
And for Actors just starting out, or Stage Actors, who have no Acting for Film experience, not to worry, you can still get a showreel made. What you want to do is pick scenes from Films, TV Shows, Plays or even write your own scenes, and act in them and get them filmed. So again, pick contrasting scenes that will show you off as an actor. Get in touch with Independent Production Companies, or even friends who are studying Film, and get them to film it. Once you have a friend or company ready to film it, you will need other actors to be in it (unless you want to film a monologue) so get in touch with Actor friends, or put a Casting notice in sites like this, advertising sites like Gumtree, or even on Facebook/Twitter.
Them once you have your Showreel finished, start sending copies to Casting Directors and Agents (note that if you send them a disk, they will rarely return it unless you send a SAE so make sure you have plenty copies of your showreel!) You put your showreel on a site, such a Youtube, or make a website for yourself as actor and post your Showreel on it - them you can send Directors/Agents links to your showreel via email.
But just remember, a showreel will not guarantee you work, but it will get your face and talent shown to Agents/Directors and increase your chances. Just don't let the no's or no responses get to you, keep trying, and you never know what might come your way.