Well i've been through this process .. from H1B to Greencard and I can tell you there is NO easy way to do it..

The ONLY option you have available to you initially is to find an employer that is prepared to file a request for non-immigrant worker.. this is a great deal of work for an HR department to go through and MOST wont do it.

I got here by having a contract house take me on as W-2 and paying my lawyers fees and application fees.. it took SIX years and an H1 extension before my greencard was approved..

Right now its going to be practically impossible for you to get a job in the US, they have to demonstrate that there are no US workers available.. and there are quite clearly plenty right now...