What steps should I follow in order to be able to start conducting research if there's no sign of support within my department?
It'll certainly be easier if you can find a professor willing to supervise you, so I strongly suggest that you keep trying on that front. But even if you can't, all is not lost! Here are the steps I recommend. Note that this may not be the only way to get started, but it's a way that works for many of my students:

Step 1: Start by identifying an area of interest

A good way to start is to identify a topic in class that interests you. Approach the professor for that class and ask him/her to suggest some related papers for further reading.

Step 2: Get a better view of this area

Thoroughly reading those papers may take a while, since this is new to you. Don't be discouraged by this! After you have a reasonable understanding of the papers suggested by your professor, start to branch out: look up the papers cited by/citing those papers to get a broader view.

Step 3: Reproduce some existing results

Somewhere in all this reading, you'll come across something that really interests you: a proof, a design of a system, a software implementation of an idea. See if you can reproduce this result (by going through the steps of the proof, writing your own software, running a simulation, etc.) Again, this may be more difficult than you expect; don't get discouraged.

Step 4: Do something new

Now that you've reproduced someone else's results, can you extend them? Is there a small variation on the system design that could improve the results, an interesting application in another domain, a stronger result you can prove? Get to work. 

Step 5: Communicate your results

Congrats, you are now almost a bona fide researcher! Go show the professor who recommended the papers what you've been working on. A big part of doing research is communicating the results, once you have something to show. (And to get into a good grad school, you'll need to impress some potential letter writers.)

You should also consider writing a draft of a paper and soliciting feedback on it.