one way to find the type of edition is looking on the title bar of the browser window. Is there any other way to find it out? though it is very basic question, but i need to know it.
Click on Your Name -> Setup -> Administration Setup.
Top of the loaded page you can see which edition you are using. .
WSDL checking option to identifying the Salesforce edition based on @KeithC's comment. Checking at the Administration Setup is the best option to identify the edition.
Once you have successfully logged onto SFDC ORG, the browser window/tab title (Salesforce.com - will provide you with the edition like Developer, Enterprise, Unlimited, etc. you have logged in.
For Firefox (refer below)
For IE (refer below)