Daycare facilities are known in Dutch as Kinderdagverblijf. Note that waiting lists can be quite long as places are limited. Lists can be found at http://www.kinderopvang.pagina.nl or http://www.babymap.nl/. You must be a legal resident to use these services.
Not all daycares have English-speaking options. Day care websites rarely list their rates so if in doubt call the particular service or consult with Blue Umbrella (website below). As a very broad estimate, expect to pay between €6.50 and €10 per day.
English speaking options include:
Baboffel Centrum Amsterdam
Keizersgracht 699 sous
Starting from 12 months and able to walk.
Derde Kostverlorenkade 34
Also you may with to contact Blue Umbrella for more assistance as they specifically help expats with child-minding issues. http://www.blueumbrella.nl
Parent and Child Groups
MOPS in Holland
Support group and nursery for 0-5 year olds. Meets every week on a Thursday. For registration and contact info see their website.
Au pairs and nannies are common in the Netherlands. Many students and young people from all over Asia, Europe and North America come to Amsterdam to work as au pairs. For child care only, nannies earn in the region of €12-€16 per hour (€480-€640 per week or €1900- 2500 per month) though this of course depends on the individual and the services provided.
Live in au pairs are best hired through an agency. The benefits you will need to provide usually include health insurance, perhaps travel and often language courses, so the benefits will often cost more than the expected salary.
Due to the large number of students eager to earn some extra cash it is possible to find listings on craigslist Amsterdam (http://amsterdam.craigslist.org) and on community notice boards in the supermarket.