Okay, so you don't understand the science behind time machines, and you haven't made the cut as a Dr. Who companion. (At least, not yet.) Plenty of opportunities for time travel still exist, even if you're traveling on a shoestring. (Pretty sure there's a joke about string theory in there somewhere, but it would take a better writer than I to land it.)
Time Travel for the Budget Explorer:
Read - This is almost a no-brainer. The more widely and deeply you've read, the better you understand the events, literature, music, and art of any given historical period. If you read deeply enough, you will almost begin to feel that you've lived it yourself. This is the first step toward real time travel.
Travel - Next, travel where you read. Stand atop Masada feeling the thump of the Roman battering ram. Walk London streets as the bombs fall. Listen for the cheering crowds in the Colleseum and the boots in Red Square. Stand still enough to hear "Th' inaudible and noiseless foot of time."
Dream - Devotions first thing in the morning, CNN running while you get ready for work, radio blaring in the car, earbuds in while you exercise, audio books while you clean, podcasts in the afternoon, TV time in the evening, and a book before sleep. All well and good, but when do you think? When do you pray? When do you process and question and dream? If the answer is never, then you have a problem.
Unpack your schedule and readjust, this time leaving some breathing room. If you can't do that, then you have a bigger problem than your inability to time travel.