TL;DR: To monitor or review a Bitcoin transaction, either check the wallet to view transaction details or use a block explorer—a tool that displays blockchain transaction data. Block explorers allow users to trace money flow and transaction history by entering the transaction, block, or address into its search fields. You can use public versions like mempool.space or blockstream.info; many users also opt to run their own block explorer instance.
If you have recently made a Bitcoin transaction or are waiting for on-chain bitcoin to be received, there are two ways to check it.
The first step is simply to check the corresponding wallet. You should be able to see the transaction in the transaction list and tap on it to expand the detail view. The second method is to use a so-called block explorer—software that accesses the blockchain and gives you all the details you might want to see. It allows you to traverse the blocks and transactions and trace the money flow pertaining to the transaction, i.e., which UTXOs the money came from and in which subsequent transaction it is used. To check any transaction, block, or address, enter it into the search field of the block explorer website.
You can even run your own block explorer instance (usually part of node software distributions like Umbrel, RunCitadel, or Raspiblitz) or access a publicly accessible version of that same software at mempool.space or blockstream.info.