Aquila, first off, congrats on dusting the bike off and getting out there. It sounds like you're doing great. I, too, started cycling again relatively recently so I understand where you're coming from. I think my first ride last year was in early June and was about 7 miles long. I ended the year with over 2,000 miles.
I've read fairly consistently that you slowly increase your mileage by about 5-10% each week. That said, I think the most important thing is to listen to your body. I have to admit that I regularly exceeded the 5-10% last year and increased my mileage relatively quickly. My pattern was to increase my mileage (both weekly and per ride) for several weeks and then take a week or so easy when I could feel my body starting to poop out on me. That worked pretty well for the most part.
I would further note that part of the challenge of riding longer and longer distances is recognizing your hydration and nutritional needs. I find that for rides of about 35 miles or less, I can get away with just drinking water. As the mileage increases from there, so too does my need to stay well hydrated, ideally with both water and a sports drink. I also usually need to eat something here and there. The longer the ride, the more I need to eat and drink. The longer the ride, the more I need to make sure that I'm well fed and hydrated before the ride as well. That topic deserves it's own thread, but I throw it out there as a head's up for your training.
As for pedaling at different speeds: Your friend might be referring to "cadence"--the number of pedal revolutions per minute. Because most bikes now come with multiple gears, you can pick and choose a gear that allows you to "spin" at a comfortable rate, i.e., a rate that allows you to balance your aerobic capacity and leg strength. Some people are "spinners" (they spin at a relatively high cadence) and others are "mashers" (they push a big gear and spin at a lower cadence). One common rule of thumb is that you should spin at or around 90 rpm. Again, it's all about personal preference and what feels right to you.
Last year, I preferred to use gears that allowed my to spin around 90-95 rpm on a flat road. As my legs have gotten stronger, however, I'm comfortable spinning a bigger gear at a lower cadence too. I will, say, however, that learning to comfortably spin at 90 rpm is a good way to protect your knees and to exercise at an aerobic, verson anaerobic, rate.
I would note that there are bike computers out which include a cadence feature, but you don't necessarily need one. You can either manually count your pedal revolutions or just develop a feel (as most us eventually do with or without a cadence monitor) for your gear/spinning preferences.
Good luck and have fun!
Kate
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher