try to start out with short rides at a moderate pace, it's pretty common for new riders to go too far, too fast, to quickly and end up with knee and/or hip problems (i'm guilty of this as well). i'd recommend starting out with short distance rides, maybe 15-20 km, and focus on keeping your cadence between 80-100. you don't want to feel like you're mashing down on the pedals as that can lead to knee problems pretty quick.
slowly increase your mileage, give yourself the occasional day or two of rest, and you'll be riding longer and faster before you know it.
you'll see the biggest gains in speed and distance early on (first few months). i started out doing rides of about 15-25 km, holding a pace of about 23-24 km/h. now i'm easily doing rides twice that long and can hold a steady pace of anywhere from 30-35 km/h (depending on wind speed and direction) and doing intervals with a pace of about 40 km/h with rest periods in between.
something else you should focus on is stretching. if you're not very flexible, try to stretch at least once a day. start out with your handlebars up high and as you become more flexible, you can start to lower them (by flipping the stem or removing spacers from beneath the stem).
and most importantly, just have fun with it. good luck