What are some possible job opportunities as an engineer? Where do I start after college?

Alyssa,
Here is what I do. As a mechanical engineer I review designs for airplanes' mechanical systems to see if they meet the regulations for safety. For example, large airplanes for passengers fly high up in the atmosphere. If they lose pressurization at high altitude they need to have supplemental oxygen for the passengers that can be used during the few minutes it takes to get the airplane to a breathable altitude. The U.S. Code of Federal Regulations has a subpart regarding this kind of equipment and Sec 25.1441 tells manufacturers what standards to meet. See the regulation:
http://rgl.faa.gov/Regulatory_and_Guidance_Library/rgFAR.nsf/0/B630761106B6D1EB85256673004DF8B0?OpenDocument
This one also sends you to look at other regulation sections. You can find those in here:
http://rgl.faa.gov/Regulatory_and_Guidance_Library/rgFAR.nsf/MainFrame?OpenFrameset
So, when I look at the drawings and they list the parts (like the oxygen supply) I have to confirm that this equipment is suitable. They may have to test it or show that it has been tested and show me the results. Then, when it is all installed, they need to test the system in flight.

You could be reviewing design, you could be designing (drawing, picking materials - say steel, aluminum, plastic, selecting parts), you could be testing your design or someone else's. Think of all the stuff we use every day or less often (like rockets). Except for the plants, animals and minerals, everything was designed by people.

I recommend that you look at job openings in companies, big ones and little ones (Apple, Microsoft, Boeing, FAA.gov, things you use) and read the 'careers' descriptions for what they look for in engineers to get an idea. Some have internships or 'entry-level' positions. Best wishes.

https://search.epa.gov/epasearch/epasearch?querytext=Engineer&areaname=&areacontacts=&areasearchurl=&typeofsearch=epa&result_template=2col.ftl