The town has one main road filled with restaurants and shops. However there are many smaller bars and restaurants hidden around Corralejo's harbour and back streets. The secret to a great night out in Fuerteventura is timing. You need to embrace the Spanish way of life and slow right down. People go out later for everything. You can shop until 9 or 10pm, and it is very normal to go for food once the shops shut.
At the top of town Italian restaurants La Mamma or Di Napoli serve a wide selection of good food. If you fancy venturing further, then the harbour contains a lot of seafood, Indian and traditional Spanish cuisine. La Luna is a good mix of fresh local produce and a relaxed up market restaurant. Just take your time deciding where to eat and don't worry about all the people touting.
For a chilled beginning to the evening why not try the Citrus Cafe in the centre of town, or Cafe Lounge around the corner to La Luna at the harbour. They offer a relaxed atmosphere, good food and drinks, and themed food nights. In general cafes will stay open until about 11.30pm, so they are a great starting point; but this is just the beginning.
Almost every night of the week, with the exception of Sunday, is party night. The key is to go for a late drink at the somewhat cheesy Rock Cafe (live music), or the windsurf bar Kiwi in the Atlantico complex at the end of the highstreet. Enjoy the music or the surf film and watch as the world filters into the bar. Everyone seems to end up in one of 3 places after being kicked out of Flick's at 2am (in the Alantico complex): Buddha Lounge (opposite Flick's and above Kiwi), Wakiki (down a side street near the Rock Cafe), or Down Under (almost next to the Rock Cafe).
The Buddha Lounge starts getting busy from about 1 or 2am, and plays a mixture of fiesta and European house music. With its dark Indonesian decor and open dance floor, you'll easily find yourself swept up with the party ambience and stumble home when dawn is breaking.
If you don't make it to Buddha, then Waikiki is an easy option. They offer food, pool and start the tunes late in the evening as well. Not generally as busy as Buddha, but is always worth a look in. Down Under is something of an Aladdin's Cave. It is literally down under, as the entrance appears small, but when you've descended the steps there is a massive basement to explore. They offer live music and a surfy atmosphere.
So, an evening out in Corralejo is simple, just choose how late/early you want to get in, and enjoy exploring the different scenes.