Check out the Open Street Map wiki. Here's the Beginner's Guide:
http://wiki.openstreetmap.org/wiki/Beginners%27_Guide
Since you mentioned mountain bike trails, take a look at Openmtbmap.org to get an idea of what is possible with Open Street Map data. Openmtbmap.org produces specialized routable mountain bike maps based on Open Street Map data:
http://openmtbmap.org/
Sadly, for the moment, Openmtbmap.org has maps for just about everywhere, except North America, so this will be of limited use for you. It does demonstrate one important concept of Open Street Map though: the data you upload from your tracks is saved in the database in a completely independent format. The data can be then converted into all kinds of other things, such as online maps, special hiking or biking maps, etc. The Garmin-compatible maps produced from this data are just side-projects. (This is perhaps why you could not find your hiking trails in the maps at http://garmin.na1400.info/routable.php. The maps there either do not include hiking trails, or they were updated before the hiking trails were added.)
At any rate, please do add your trails to the Open Street Map database. We can then all benefit from them. (Plus mapping is almost as addictive as Geocaching.)