The first call that you need to really work when using the AdWords API is getAllAdWordsCampaigns. Here's the minimum XML / SOAP that I've found to work. Of course, you need your own AdWordsAPI token and account.

 <soap:Envelope xmlns:soap="http://schemas.xmlsoap.org/soap/envelope/">
 <soap:Header>
  <email>EMAIL</email>
  <password>PASS</password>
  <token>TOKEN</token>
  <useragent>AGENT</useragent>
  <clientEmail>CLIENT</clientEmail>
 </soap:Header>

 <soap:Body>
  <getAllAdWordsCampaigns>
    <dummy>0</dummy>
  </getAllAdWordsCampaigns>
 </soap:Body>
</soap:Envelope>

¶ 2/14/2005