All right so I was timed out (I guess?) twice now so this really is going to be the shortest version ever.
Our natural gas water heater died (small leak that prevented pilot light from staying lit). Our water heater also supplies our central air ac/ heating system (found that out the hard way the first time the pilot light went out, but not realizing that it was a leak and not wind that caused the pilot to go out).
Almost 2 days later a company came and installed our new gas (natural) water heater (same size and specs as the previous heater).
Within an hour after install we had lots of hot water, so we turned the heat back on. 2 hours later we were still freezing (and realized that only cold air was blowing through the vents). We shut that off (thinking maybe the new tank hadn't had enough time to heat up enough water or something). I should note my husband and I are mid 20's first time home owners and no absolutely nothing about water heaters and central heating and other standard knowledge things standard homeowners probably know.
One of the guys that came to give us an estimate tried to explain the way our heating system worked (something about water from the tank going through coils that hat blowers that blew air over the coils that caused the air to heat up... or something along those lines).
My question is, could there be air in the system that is preventing the water from running through these unseen coils? If so, is there a way I can bleed them on my own? My husband and I were both too busy to call today, and I will try to call them tomorrow but as it took 1.5 days to get the water heater installed I'm not sure how long it will take them to come back and check out the heating system (or how much they are going to charge us). We will pay what we have to but as college students and my husband with a part time job we don't have a very large income to just throw around at everything.
Are there other things I should be looking for? Testing for? Any tips or tricks that would help us in this situation?
The good news is that we are not expecting snow this week and that we should have low 30's at night and high 50's during the say so it's not really an emergency that we don't have heat. We do have enough blankets, and hats and a gas fireplace that can keep us warm enough as long as we keep ourselves restricted to the living room. I just REALLY miss my bed and would really like us to be able to work at our office desks without having to wear our winter jackets.
Any and all information and or advice would be greatly appreciated. Thank you so much.

You most likely have an air blockage in the heating system. Hopefully the system isn't frozen. Since they just put the new water heater in & you have not had heat since, there should be no charge for a service call. They failed to do the whole job of making sure every part of the system functioned as it should.

Thank you so much for responding so quickly I really appreciate it!

Please keep us up to speed on your progress.

I apologize for not responding more quickly (our internet was down all day yesterday). I called the service number and tried to explain the issue but was passed around to 3 different people all saying it was impossible for the heating issues to be related to the water heater and that I had to have a furnace somewhere else. Eventually they said they could send a guy out on maybe Friday but most likely it would have to be the weekend or the following week and they were not certain if the guy would have time. I was also told that I should be prepared to pay the $140 for the visit if it was indeed unrelated, as they believed it to be. I told them I would call back to schedule an appointment as I wanted to speak with the property manager and my husband before I was lead round and round and charged money (that I didn't have) for something that could be easily fixed if the person was knowledgeable.
It turns out all the units in our housing development have a hydronic heating system (so it does use the hot water heater). When I called the number back to reschedule I was instructed to leave a message. I did but was never called back (nor did anyone answer the phone when I tried to call again later that afternoon/ early evening. We were once again without heat. The next day I tried to call back but no answer so I took matters into my own hands. I researched the heating system online, found the ceiling panel in the downstairs bathroom and, with my husbands help since I was not strong enough or tall enough to remove the panel or reach the pipes, we bleed the pipe of air. Within an hour we had full heat, problem solved. I called the company back again (still no answer at the extension of the person I spoke to previously) and spoke with the receptionist asking her to pass along to "Mike" that I was no longer in need of a service man to come to my home and that the heating system was hydronic and thus the lack of heat in my home was due to the water heater replacement they did for me earlier that week.
I have no idea if he received the message or not but as I have not heard back I can only assume that he did (that or he never checks his phone messages). Sadly, after all of that I woke up Saturday morning to find my ferret dying and there was nothing I could do to save her. She wasn't sick (no sneezing, or coughing or abnormal bowl movement). She was perfectly fine the week before our water heater went out and we did our best to move her cage next to a lamp to help supply heat to her while we covered her cage in a blanket. After fixing the heat problem ourselves she seemed to show signs of recovery (as a female she has always been very small but her eating habits remained normal. My husband believes that it was the additional 2 nights without proper heating that did her in (that her body worked too hard trying to stay warm and that the severe cold (that has my husband and I huddled for warmth took too much of a toll on her poor little body).
I digress. The good news is that we managed to get heat back before it snowed. Bad news, we lost a pet. I've at least learned my lesson and will spend much more time learning about every inch of my home, never again running the risk of knowing so little that I put all my faith into a professional's words of completion or that I am wrong about something I knew to be correct.

I'm truly sorry for the loss of your pet ferrett.
I would certainly WRITE to the service company which replaced the water heater & express my displeasure with their service. Be sure to keep a copy of the letter & if you get no reply from the company within a reasonable time (10 days?), I'd report them to the local Better Business Bureau & government authority having jurisdiction over that type of service company.