Just to add to wilbill's reply:
When you right click on the tile, the number of shields, food and gold it says is the number of each it will give you if a town's citizen is assigned to that tile. If it is plains beside a river it will be 1 food, 1 shield and 1 gold, so you will get one of each.
If you irrigate the tile you will get 2 food, one shield and one gold
If you mine it you'll get one food, 2 shields, one gold
If you build a road you'll get 2 gold instead of one, and this can be in combination with either irrigation or a mine. You cannot, however, have both an irrigation and a mine in the same tile.
Your question implied the idea that irrigation or mining were needed to get the food, shields or gold; this is not the case, they just, as wilbill said, increase what you get.