Assuming you are using android....

Using your file manager app locate the downloaded file and click on it (or click and hold)

You should get prompted to open the file using........ A list of possible apps on your phone

Select Osmand 

Make sure it's a gpx file downloaded, I don't think Osmand plays with tcx files

Or using File Manager, move the gpx file into folder : Android/data/net.osmand/files/tracks 

This folder will be where your maps are stored - either in internal storage, or on your removable SD card