We didn't realise quite how much hard work it was to do this as previously we'd been lucky enough to have a broody hen to do all the work for us! It is quite an undertaking (especially if you have to manually turn the eggs) but hopefully it's worth the effort!
To hatch hen eggs, you'll need to provide three things: the correct temperature, the right humidity, and also turning of the eggs. And you'll need to do this for 21 days as that's how long it takes for a chick to grow and hatch!
An incubator is usually an insulated container with a heater and water trenches which you fill to the correct level to provide the right humidity level - there is usually a vent that you can open and close to alter the humidity too.
The correct temperature for hen's eggs is 38°c, although slightly below or above should be ok, you should try and get it as near as possible, as it can cause deformities and death if it's too far from the ideal temp.
Most incubators have a thermometer built in so you can fine-tune the temperature to the exact one you need. Remember to give the incubator a few hours to get up to temp when first turning it on, and leave it a while before re-checking the temp after you adjust it for it to settle down.
The humidity is harder to keep an eye on, unless you have the correct (and expensive) measurement tools, or precise weighing scales which you can measure weight loss in the egg, you have to go by "rules of thumb" - in the incubator we are using (a Brinsea), there are two water channels, and for hen's eggs you only fill one of the water channels, and set the air vent to half-open.
Turning the eggs is very important and many incubators do this automatically. If yours doesn't, then you need to turn them at least 3 times a day, although you can do it 5 times if feasible. You turn them an odd number of times so that they don't sit the same way each night.
A couple of days before the eggs are due to hatch, stop turning the eggs (the chicks need to get into the right position to hatch!), and increase humidity by filling both channels with water and close the vent to allow maximum humidity to aid hatching.
Once you hit day 21, don't panic if nothing hatches yet - if your temperatures are slightly out it can mean your eggs hatch earlier or later than they should.
You leave your newly hatched chicks in the incubator for a day or two to fully dry out after they hatch, then transfer them to your brooder box (a container with a heat lamp) - they'll huddle under the lamp if too cold and away from it if they're too hot... Start them on 'chick crumb' and before you know it they'll be growing real feathers! You 'wean' them off the heat lamp by gradually moving it further away from the brooder every day until the growing chicks are hardy.
It's a lot easier to get a friendly hen to do all the hatching and nurturing for you!