My usual adage that the Boston companies are always hiring has been proven to be untrue right now... Several of my friends trying to go up for jobs have proven it to be very hard, but after relenting, have been successful. You needed to start the process a few months ago.
Start by filling out and printing an application for all the companies you are interested in. Submit those you can, hold on to those you cannot. Make sure the application is fully filled out and ready to go. Give the company 2-3 weeks to get through their stack, and if they have not called you, give the HR director a ring.
If you come up empty handed, consider dropping by their headquarters. While you are there, seek out the HR person. Come, introduce yourself, ask ask what the next step in the process is. Some companies are more receptive to this visit, and have been known to offer you a job on the spot. Make sure that when you come, you are dressed appropriately (search for uniform attire on this forum). Bring a copy of all your certs (EMT-B, CPR, DL, etc), a current resume, and maybe even a copy of your driving record (no less then a month old, you can get it from a local RMV).
Be prepared for an interview, or nothing. Sometimes the HR person is out, and you may have to come back. Do not be bothersome or annoying, but persistent. While you are at the HQ, talk to the crews that are around, ask what they like about the company, what the calls are like, what the shifts are like, what the trucks are like, etc... For some basic analysis of some of the companies, search on this forum.
If/when you see a truck from a company you are interested in on the road, consider going over and talking to the crew (presuming they are not on a call). Ask how they got hired, when, what circumstances, how well they know the HR person...? What does the company look for in an employee?
If/When you get hired, ask when the next orientation is, how soon you can start working, what they expect of you before you start working, etc.
Hope all of this makes sense... its a tough world out there, but with a little patience, you may succeed.
Good Luck!
Dan