There are a few options you can look at when wanting to ensure your WiFi reaches your new space.
If your outbuilding is close to the house, depending on where your router is located, you may find a booster or extender that will be sufficient to make your WiFi signal reach. These devices need to be close enough to your home router to work. This is the cheapest option, however, the drawback to this is that this solution is not very reliable, and you could still have frustrating connection issues which may drive you to a different solution after spending the money on a cheaper extender or repeater.
If your outbuilding has power, another option could be a powerline adaptor. This works by using the power cable to transmit your internet connection. This is another affordable option; however, this method can have interference problems and again may leave you with connection or speed problems.