I have a new bike that I've been riding for about a week now, & riding is a lot tougher than I remember it being when I was a kid! I can't ride very far yet but I like to do interval training within the time I do ride, such as the Tabata method. The Tabata method, if you aren't familiar with it, consists of all-out hard work for 20 seconds followed by 10 seconds of rest which goes on for four minutes.
So what I do is pedal as hard as I can (or as hard as I can without fear of crashing) for 20 seconds, then coast for 10 & repeat for a total of 8 cycles. It's a simple concept but it's really effective.
Here's an interesting article about it, and
another.
This is an article on several different interval training methods for cycling.