UTXO can only be spent completely.
This happens by claiming them in the Transaction Input Script and requires a valid signature corresponding to the address the UTXO is associated with.
The transaction inputs' value is then reassigned by the transaction to create new unspent transaction outputs. Usually, there are at least two outputs, one going to the recipient of the payment, and a change output going back to the wallet of the sender. The sum of the assigned outputs must be smaller than or equal to the sum of consumed inputs.
Any amount that doesn't get assigned to new outputs can be claimed by the successful miner as transaction fee in the Coinbase transaction of the block the transaction gets included in.
When a block gets found, all nodes in the network enact all the transactions on their UTXO set, marking the inputs as spent and replacing them with the newly minted unspent transaction outputs.
Bitcoin really doesn't have a notion of "coins" as individual objects. There are only transactions which can be of arbitrary amounts. – Nate Eldredge – 2016-01-28T17:33:52.363
Yeah, I "kind of" understand this, but how can the UXTO be built anyway? – Henrique Barcelos – 2016-01-28T17:39:10.377