What are the economics of confirming a block of transactions?
Mining a block (also called confirming) is not dependent upon the number of transactions in the block. A block with a single transaction is just as hard to mine as one with 1,500 and earns you the same reward.

In addition to the reward, miners can claim a fee, which practically is the difference between the sum of the inputs and the sum of the outputs. The rule to compute whether a fee is required can be a little complicated. The person issuing the transaction is free to include a fee or not but a transaction that doesn't may not get confirmed.

Finally, the mechanism by which reward and fees are claimed is by inserting a transaction in the block, in the first position, that sends the total amount to the miner's public address. The network validates it with all the rest.