You should only hear 6 clicks: 1->2 , 2->3, 3->4, 4->5, 5->6, 6->7 when shifting up on a 7 speed system, and reverse the arrows when shifting down.
If you can't shift through all the gears, check that the derailleur is not bent, you have adequate cable tension, the low and high limits are set correctly (these should be a set once and forget it thing) and then play with the indexing adjustment (the barrel adjuster at the derailleur). See this link for more details. If your cables are old and rusted or kinked, you may need a new shift cable as well.
If you just purchased the bike from a shop, they should adjust it for you for free if it was recent.
Note that these are cheap shifters, so if there is indeed something wrong with the shifter (e.g. you meant to say you were only hearing 5 clicks), you're going to have to throw it out and buy another one for around 15 dollars.