WebRequests can be instantiated like any other object. Two constructors are available:
UnityWebRequest wr = new UnityWebRequest(); // Completely blank
UnityWebRequest wr2 = new UnityWebRequest("http://www.mysite.com"); // Target URL is set
Is something described here not working as you expect it to? It might be a Known Issue. Please check with the Issue Tracker at issuetracker.unity3d.com.