Bishop, I'm not an engineer, but I do work with them (as a CAD Drafter), but I've worked with enough and have met enough engineering students (attempted a Civil degree, failed at Calc 4) to know that an internship in the environment you would like to work in is the best place to start. Knowing that you're graduating this coming spring, however, puts you at least a year behind most in terms of finding a good internship, at least if I put you in comparison to the intern my work brought in over the summer.
My suggestion would be to check around the local city/county/state websites to see if anyone is offering an internship, and if not, go in and offer yourself for free. It might be a tough swallow to take a job right now without pay, but sometimes getting your foot in the door is the hardest part. If you work at it as if it's a real (paying) job, you could very likely get offered a job. I only suggest looking at the public sector jobs first because, at least as a drafter, it's been the best paying job I've ever had, with benefits that are far better than the private sector. Maybe because my job puts me in a union, but right now, I've got absolutely no complaints.
Outside of the public sector, the same rules apply... check websites for job postings, internship or not, and some good old cold calling can yeld you some good results. I would suggest though that you actually go into the engineering office and offer up a resume, rather than calling and asking. Find 5 or 6 offices in a specific area, get dressed up like you would for an interview, and go out and offer your cover letter, resume & references.
If it's a small company (25 or fewer employees), go in and ask if you can talk to the owner or one of the engineers... don't settle for the office manager/receptionist if you can (they just tell you not hiring and will file your resume in a folder that hardly ever gets opened).
If you have a specific company that you think you'd like to work for, call them up and ask for an informational interview with one of the engineering, preferrably one in the area that you would like to be in (don't schedule an II with a structural engineer if you want to get into that company's civil side). Ask them about their company, their job outlook, and ask the engineer if he has any non co-worker colleagues that might be hiring or that work in a similar company.
Craigslist, job fairs, and the good old fashioned newspaper are also good links. I've gotten a job from each of them.
Do you participate in some sort of an organized team sport? I got a job through a soccer teammate's wife who worked in an engineering firm's marketing department. That job didn't last very long unfortunately, but I ended up making a contact at the city's engineering department that ended up fleshing out a future job that I found.
Finding a job is all about getting yourself out there. It's not a great time to be looking for a job in the Engineering field (at least not where I'm at)... There's more people looking for them than there are spots to fill, and those spots are not going to come looking for you.
Best of luck to ya though