By train
Haarlem is well-connected by train, with intercity and sprinter trains running between Amsterdam and Haarlem Central Station roughly every 10 minutes. From Amsterdam, it's a 15 minute journey (€3, 80) with trains usually leaving from platform 1 or 2. Pay a bit of attention: Haarlem is one of the stops on the main train line between Amsterdam and Dordrecht/ The Hague, so it will likely not be the final destination for the train. However, as not all trains to those cities will stop in Haarlem, check the signs or ask a conductor to make sure you're getting into the right one. Coming from Schiphol directly, you'll have to change once, at Amsterdam Sloterdijk (or at Amsterdam Central Station, but that will take you an extra 10 minutes or so). Trains are easy to use and you may be lucky enough to encounter one or more of the most entertaining ticket collectors in the country. They number singers and magicians amongst their members.
By bus
A good alternative is to use the big red and grey "R-net"-bus, line 300. It runs every 6-10 minutes between Schiphol and Haarlem Central Station, or you can get out at Wulft/Centrum. There are a fair amount of stops along the way, but for a lot of the journey there is no traffic because the bus has its own dedicated lane. The trip is approximately 45 minutes. You will need to carry your luggage on the bus with you. As on all public transport in the Netherlands, you pay with an OV chip card and a single trip costs € 3, 64. There are many bus stops clustered in this area -- the one for the R-net 300 is across the street, and is indicated on the sign at the bus stop.
By bike
If you have – or rent – a bike, it takes between an hour and an hour and a half to cycle (depending on the cyclist) from the centre of Amsterdam, a fairly relaxing ride on typically level terrain
