When you first start cycling, you will probably read about the speeds and distances travelled by other cyclists, and find that you fall a long way short. Many experienced cyclists will cover 60 miles at 20-25 miles per hour a couple of times a week, enthusiasts much more, and faster.
This knowledge often translates into a desire to push yourself hard, when you can only manage 10 miles at 14 miles per hour!
The first thing to realise is that cycling is a long-term sport. Over at least the first three years your muscles gradually change to become accustomed to these greater speeds and distances, and you will not do the same after three months as you will be able to after three years.
For the first few weeks, just get used to the bike. Go on gradually longer rides. There is no shame in only doing a few slow miles at first, and I promise you any cyclists that go racing past you will not be thinking how useless you are. They might be thinking how good they are, but that's not a problem for you.
After a few weeks on 'normal' terrain, going out two-four times a week, you could aim to be covering 15-20 miles, perhaps a little further at the weekend. When it seems appropriate, try and go faster, but don't pressure yourself.
A typical beginner speed is about 14 mph, and most cyclists would be achieving that average after a few weeks, if not straightaway. You might be a natural, or live in a very flat place, in which case it would be higher. Perhaps your genes make you a natural and with very little training you'll be whizzing along like Lance Armstrong. Probably not, unfortunately.
Having become accustomed to spending an hour at a time on the bike, you could now try a ride of 2 hours at the weekend, and keep going on the shorter rides during the week.
Broadly the two targets for your cycling training are (1) speed and (2) endurance. So a good mix of rides is perfect - short rides where you work hard, to increase speed, and longer rides where you don't worry much about speed but gain the experience of sitting in the saddle and cycling for reasonably long periods.
Increase things slowly, and above all don't spend too much time looking at your average speed. A breeze, a hot day, whether you are in a good mood, or a bit tired, all these things affect your speed, so you can't expect to always improve on the time before. It really doesn't matter - speed and distance will come, if you practice regularly.
That's not to say you should take it too easy, of course. You should feel if you have done some exercise when you have finished, with aching legs but not legs that give way under you. You shouldn't feel as if you could easily repeat the same ride straightaway!
So overall the message for your first season of bike training is, try and cycle regularly, and with a reasonable amount of effort. Slowly build up speed and distance as the weeks and months pass, but don't overdo it.