To collect traces suitable for use in OpenStreetMap, you'll need some kind of GPS receiver that's capable of recording a log of locations over time, known as a track log, trace, or breadcrumb trail. This could be a hand-held GPS receiver, a bicycle-mounted unit, a combination of a GPS receiver and a smartphone, or in some cases a vehicle satellite navigation system. There are also some dedicated GPS logger units, which don't provide any navigation function, but merely record a track log for later processing. You'll also need some way of getting the recorded traces off your receiver and onto your PC. This could be a USB or serial cable, a removable memory card, or possibly a Bluetooth connection. There are reviews of GPS units by mappers in the OpenStreetMap wiki.
There are also GPS receivers designed specifically for surveying, which have very sensitive antennas and link directly into geographic information systems (GIS). These tend to be very expensive and less...