The easiest and quickest way is by train. Edale Station is located on the Hope Valley Line from Sheffield to Manchester Piccadilly, with direct trains every hour in each direction. There is usually one train an hour in each direction (although be sure of this before setting off), the journey time from Sheffield is 33 minutes and from Manchester, 43 minutes.
Edale Moorland Centre. This visitor centre features exhibitions and interactive exhibitions about the surrounding moors. Entry is free and it is located a short walk from the station on the road leading from the station to the village. As of 2015, the centre is open daily until the 30th of October, open weekends in November and closed in December and January (with the exception of 26/12-3/1).
The Church of the Holy and Undivided Trinity is also located on the road between the station and the village (slightly further up from the visitor centre). Built in 1886, it is a good example of Decorated Gothic architecture and is a Grade II listed building.
Jacobs Ladder. Located a 25 walk away from the village, it is a steep zigzagging path leading up one of the hills surrounding Edale. It is historically significant for being located on a pack-horse route connecting Liverpool and Manchester with Sheffield. Great views over the Vale of Edale can be had from the top.
One of the main attractions of Edale is its proximity to many good hiking routes, in fact it the starting place of the Pennine Way. If feeling energetic, you should make the most of your trip to the village and hike up one of the surrounding hills, nearby hills include Mam Tor, Kinder Scout, Lose Hill and Win Hill. If travelling by public transport, then it may be a good idea to start your walk in Edale and finish somewhere else, for example if travelling from Sheffield, it would be easy to start your hike in Edale and walk to the nearby popular tourist village of Castleton via Mam Tor before catching a bus back to Sheffield. From Manchester, you could catch the train to New Mills and hike to Edale via Kinder Scout and catch the train back to Manchester.
There is a small cafe next to the train station that sells snacks, sandwiches and drinks. The post office in the village also sells a variety of snacks and drinks, as well as all the other items you'd expect to find in a small convenience store.
Sheffield is a relatively short train journey away, once known for its steel industry, it has become a hotbed of culture. Home to the largest theatre complex in the UK outside of London and with a large and famous music scene as well as two large universities. Until recently it was the only British city to be partially located inside a national park and is home to more trees per person than only other city in Europe.