All you really need is a text editor :-) but you'll find that using a developer toolkit can save you lots of time until get used to the WAP environment.
  
But first of all you should visit the authoritative source for all things WAP; WAP FORUM.
 
Registering yourself with the Nokia WAP Developer Forum and then downloading for instance the Nokia WAP Developer Toolkit should probably be one of your first steps. The toolkit comes with PDF files that will give you references on the WML and WMLScript command syntax and general WAP insight. The Nokia kit requires JRE (Java Runtime Environment) v.1.2.2 or higher. A link is available at the same location.
 
Note that a toolkit might be designed for developing applications for WAP devices in general, not mobile phones in particular. What you make with a WAP developer kit may look nothing like what you get when used from the micro browser in a mobile phone. To be sure things look the way you want, you either need the actual WAP device, such as a mobile phone, or an emulator.
 
Nokia has an emulator for the 7110 phone which comes with the Nokia WAP SDK 2. The emulator is in effect identical to the 7110 it emulates - including the bugs, and in this case that is a good thing because you want to avoid them. The Nokia SDK also includes a small WAP server which lets you read WML decks off local drives or any HTTP server.
 
Register and check out the Phone.com developers site. Phone.com provides the UP.browser which is as far as I know the most widely used browser, especially in the US. Phone.com provides a UP.SDK available for download, after you have registered.
 
For the Ericsson R320 and the R380, which is available early in 2000, you should register and check out Ericsson's Developer's Zone for developer kits etc. For the R380, there's a very good emulator available at Symbian available for download without the need to register at the Ericsson Developer's Zone. Ericsson does not seem to have a publically available emulator for the R320.
 
Motorola has a platform called Mobile Internet eXchange or MIX for short. The Mobile Application Development Kit has development tools for both WAP and Motorola's VoxML. After you have registered, the package is available for download at http://www.motorola.com/MIMS/MSPG/cgi-bin/spn_madk.cgi.
 
WAPmine has a stand-alone application called WAPPage which is a WYSIWYG editor with an XML tree view for editing WML code. Requires only limited knowledge of WML tags.
 
If you are developing applications for the public, you want to test these applications on as many WAP devices (or their emulators) as possible. Just as you would test your HTML documents on several browsers. Note that the differences between two WML micro browsers will be much more noticable than the differences between two HTML browsers.