OSM map on my website

I run a small website for a walking group. I would like to add to my walk descriptions by including my own GPS traces on OSM map sections without including any other traces in the same area. Does anyone know if this can be done?

Maybe you can get some inspiration from the examples listed

at http://wiki.openstreetmap.org/wiki/Track_drawing_websites ?

Thank you, I will have a look at the link.