There are a few tricks that will save you some euros when booking KLM flights. First of all, if your flight leaves from Amsterdam, you'll pay a 10 EUR booking fee for each booking you make on the KLM website. You can avoid that fee by booking on airfrance.nl instead. There is no booking fee there, and you can make almost identical KLM bookings. If you plan to purchase hold luggage, make sure you enter the Flying Blue program. You're entitled to a (substantial) discount on hold luggage even with the lowest tier of the FB program. UPDATE: it seems that nowadays KLM's lowest fares aren't available on the Air France website, favouring lower indirect flights via Paris.
If you live in Belgium or in the south of the Netherlands, you might consider travelling from Antwerp or Brussels (use 'airport' names ZYR or ZWE). As you don't have a direct flight in such a case, the price will often go down compared to travelling from Amsterdam. But you need to prove that you actually use the dedicated train to Schiphol, otherwise you'll have to pay the original fare. On the way back, you don't need to bother. You can just head home and not use the train.
On routes where KLM competes with low cost airlines such as easyJet, you'll often have the opportunity to book one way fares at more acceptable prices than you'd usually expect from a legacy carrier. This can come in handy. For instance a flight from Zurich to Amsterdam can be booked on easyJet, but there is a very limited schedule. With KLM, you can choose from many options a day, at still acceptable prices.
UPDATE: In the KLM app, at least in its large format on the iPad, a free 24 hour option to keep a certain flight against the current fare is available. On the desktop website, there are only paid options.