When you start to run a bit further, you may wish to consider taking a water bottle or another hydration option with you on the run.
You may want to take water, or a sports drink or even, for even longer runs, some nutrition like energy gels or small bits of powerfood.
When looking for hydration / nutrition options you may wish to consider whether you wish to carry a bottle in your hands or not and how many bottles you think you'll need.
As you see below there are plenty of hydration options, fuel belts, camelbaks, etc.
My preferred option is the fuel belt, especially the four-bottle one. It allows you to distribute the weight quite evenly and as such allows you to carry enough with you without it ever getting really inconvenient.
I always find that the first 2-3 minutes of running with the fuelbelt is a bit annoying, but then you forget it is there and you can run easily with having the convenience of drinking a little bit of water every 15 minutes!
I hope this page helps in making up your mind about which hydration options you should choose.