Deia is a small town and easily explored on foot. It's the getting there and away that can prove more problematic, especially if you are using it as a base for other day trips. There are no trains to this part of the island and if you're hoping to do the trip by boat, be prepared for a long hike uphill to get to the centre of town.
The buses in this seemingly remote outpost of the island are actually very good and with a bit of planning it is a realistic means of exploring this section of the island (less so if you wanted to head over to the East or explore the central plains). The route connects Port de Sóller, Sóller, Llucalcari, Deià, UIB, Hospital San Espasses, Palma, Platja de Palma. They run Monday to Saturday every 15-20 minutes from 7.30am until 8.30pm, with a slightly reduced service on Sundays. See http://tib.illesbalears.cat, 647 786 886/971 177 777 for more detailed schedules.
A cab to or from Palma will cost you around €50 and you'll have no problem in finding anyone to take you. When you live on an island taxis are more than happy to make the longer trips. A cab to or from Sóller costs around €21. Expect to pay more at night.
The jet-set way to see the dramatic cliffs of Deià is by helicopter. If you're planning something really memorable for someone special, or just want to treat yourself, it's worth the splurge. Check out www.sloanemallorca.com who offer trips at €450 incl IVA for 30 minutes, and €650 incl IVA for 1 hour.
For general advice on getting around the island, see How to get around Majorca.