If you do something bleakly, you do it despairingly, with no hope and no joy. After moving to a new town, you might set bleakly off for school each day, lonely and missing your friends.
If your dad stares bleakly out at the snow-covered driveway on a winter morning, he's probably feeling hopeless about clearing it in time to leave for work. After a long drought, a farm's dry, cracked fields might seem to stretch bleakly across the horizon. The original meaning of bleak was "pale," from the Old Norse root bleikr, "whitish or blond." Later, bleak came to mean "bare and windswept," with the figurative meaning of "cheerless."