Like anything you can design & build an app yourself if you have the time to learn. An eye for design and the type of brain that likes to code help too. If you want to do it yourself you need to pick the platform you want to target (iOS/Android) or look at on of the cross platform frameworks and see which tools you need to learn to get started.
As well as the building of the app you also need to think about the design – how it looks and how it works. The market is getting more and more crowded and design/user experience is something that can set you apart from the competition. If the app is for an existing business then the user experience is even more important – you don’t want to pee off clients/customers will a slightly crappy app.
I work at an agency that designs and builds mobile apps and games so I’m going to be slightly bias 😀 But I see websites in the same way – if you are doing it for fun then have a go, if its for business then pay a pro to do it.
I’d talk to a few agencies or freelancers to get an idea of costs etc. You’ll soon get a feel for the market, and who you’d like to work with. Cost wise you’ll find a spread from kids in bedrooms, freelancers (though in our experience it tends to be freelances that are either designers OR developers – not both), small agencies then on to the big players – which I guess means from the low thousands upwards depending on where you want/need to be in that list.
Look local, but don’t rule out working with people else where in the country. We have clients all over the place (uk and international) and some of the best agencies and freelancers I know have clients all over the country (and world).
Good luck which ever way you go!