I took up harp at the age of 9 just for a hobby. My main ax has always been drums.
Anyway, the pursing of one's lips to cover a hole at a time is, by far, the most common method. Covering multiple holes simultaneously with the tongue, however, will get you specific intervals of notes simultaneously, which is handy during solos here and there. Also, tongue vibrato is a soulful tool, as well. Plus, chicks dig it.;-)
Another thing:
There's a mode called, "second position" or, "cross harp" where you're playing the root of the key by inhaling into the 2nd or 3rd hole from the left. With a "C" harp like you have, somebody playing cross harp would use it if the band is playing in "G". To figure out which key harp you'd need for cross harp, find out the key of the song, then think of that key as #1. Go up the alphabet, raising an additional finger with each letter. When you reach #5, that's the key of harp that you'd need to play cross harp for that song.
I'd also suggest listening to Sugar Blue (most famous for his harpwork on, "Miss You" by the Stones) and Delbert McClinton. (His first session ever was "Hey Baby" by Bruce Channel. Later, he toured with Roy Orbison on the same bill with the Beatles. Lennon said he'd gotten his first and only harp lesson from Delbert.)
Sonny Boy Williamson is another good blues source.
One more thing:
To break in their harps, all of those guys would soak them when they first got 'em.
Makes the notes bend easier. Water's OK but most of these ol' boys use vodka. Soaked 'em about a day. NOTE: If your harp's frame is plastic, like a Hohner Special 20 (great harp, BTW), just shake it dry and git ta gittin'...BUT...if your harp's frame is wood, you'll have to sand it a little bit because the wood will swell after a soaking...AND...AND...AND...be sure to vacuum it out before you breathe in the first time unless ya wanna lung fulla sawdust.
Have a ball, bud!