I want to use Open Street Map data but the Open Street Map website does not have these features. The main features I need are directions and turn by turn GPS navigation.
OsmAnd can work with online or offline (pre-downloaded) OpenStreetMap data. It offers offline search and directions (pedestrian, cycling and driving). It can provide voice guidance.
The basic application is free (no cost and no ads). There is a for-pay version which allows downloading more offline maps.
Locus Maps can do this and more. A very useful bonus feature here is it can import complete
.kmz files (including images and everything) for offline use, so you can make your own travel guide (used it this way a couple of times). If you calculate your routes ahead (e.g. in the hotel, while still on WiFi), navigation should also work offline.
Locus Maps supports a bunch of map sources, not only OSM, but also vector maps and more. More sources are introduced via an addon (Map Tweak).
It's good when it comes to privacy, as per default it accesses almost no private data (access to contacts must be enabled via the contacts addon), and it even has things like an AR addon (check out more).