Unless you are lucky enough to live near accommodating parents or in-laws, or you're a hermit, you'll probably find yourself searching for a babysitter at some point.
Ideally, you can save yourself a lot of cash by having some sort of reciprocal arrangement with a friend. One of them babysits for your children for an evening (or a morning/afternoon/Saturday), and you return the favour another day. This works fine as long as they do actually ask you to return the favour. A couple of my friends have babysat for my children, unpaid, on the expectation that I'd babysit for them on another occasion, and then they've never asked me to. So I haven't felt able to ask them again. If you require a babysitter a lot more or less often than your friend does, then this arrangement might not work for you.
The alternative is a wider circle of friends and acquaintances, all babysitting one another's children. In this situation it's easy to lose track of who owes who an evening, so to make things easier you can make it a more formal "babysitting circle". You'd need some form of "token" or a "book" to keep track of how many hours babysitting each person is in debit or credit, and some ground rules, such as how many hours debit you're allowed to run up, are the children expected to be in bed, should a snack be laid on, does the hourly token rate double after 11pm or midnight? You need at least six families in a babysitting circle to make it work.
Or, you can employ a babysitter. As a new parent I put in a web search for "how much to pay a babysitter" and got some wildly varied results, from £2 per hour (mean) to £8 per hour (premium London rates I think!).
I went down the middle and decided any teenager would be happy with £5 per hour, which is more than the minimum wage, and definitely worth their while to sit on the sofa, eat your snacks and watch your DVDs while your little ones snooze upstairs. Of course, if your night out begins before the children are in their beds, then the babysitter starts to really earn their cash as they struggle with manipulative children trying to wangle a later bedtime!
Not knowing the local teens, I put an advert in a local shop window, and got two responses. I asked for a character reference, but that was about it. I started to use both babysitters. One was from the neighbouring village, so while she got a lift at the beginning of the evening, we needed to drop her back after we got home. She was fine, but she didn't like to sit C (who was about a year old) unless he was guaranteed to be fast asleep (I don't blame her, he was a nightmare to settle!). The other was a neighbour in our own road. He was super cool and confident, and seemed to particularly enjoy coming over when C was awake. As we left he'd get C to wave byebye, then he'd get out the cars, put on an episode of Thomas, and then settle C down to bed.
Once Bug was born we had no need of a sitter for a few months, and by then the two sitters had gone to University, but our neighbour's younger brother was now primed to babysit, and our next-door neighbour was also old enough (we like our sitters to be at least 16), and keen. These two babysitters are both calm and capable, they usually bring along their study books, and are also working their way through our DVD collection. They are both happy to come before bed-time if necessary, and have demonstrated that they can cope with gross nappies, bed-wetting, illness, bad dreams etc.. They are more than happy with £5 per hour. We're also particularly happy to have them from our street, as it means that their own parents are close at hand if there's any real disaster, and they can easily walk home once we're back.
Having trusted babysitters has been a real bonus to us. We don't go out very often as a couple, but having babysitters available has meant that we have made the effort to do so occasionally, which is good for us. We know that the children are in safe hands. If I know somebody new in the village with young children, I always recommend my babysitters. Once we move, finding new ones will be quite high on the priority list, and I just hope that we're lucky enough to find such good ones again.