Traces are routed in segments on your layout. If you want to select multiple segments, you can use the Ctrl and Shift keys just in the schematic editor.
If you want to select all of the segments of a trace on one layer simply click one segment and repeatedly tap the 'E' key. This will expand the selection one segment at a time in each direction. This is useful if you want to delete an entire trace. The expansion will stop when a via or pad is encountered.
Alternatively if you want to select an entire net, including all vias and traces on all layers, simply click the net name from the Net List. You can use the Search box to easily find specific nets.