First, theoretical background can be found here:

Selective transparency in Monero vs Zcash

Why is the viewkey able to track incoming transactions, but not outgoing transactions?

Is there any way to construct a transaction manually?

Basically the gist is that you know a (the private view key) and R (the public tx key). As a result, you are able to compute the shared secret ( aR = D' ) and "decrypt" the transaction.

If you are using the CLI, you ought to perform the following steps:

In the CLI type viewkey , copy the private / secret view key. Go to this tool, which was created by core-team member luigi1111. Furthermore, "Note: this site operates completely on client-side Javascript; no data is ever sent to the web server." Enter your transaction ID / hash in box 1. Transaction Hash: Enter your private / secret view key in box 2. Private Key Enter your public address in box 3. Recipient's Public Address: Press on Check . If it shows This address owns output x with pubkey: y for amount: z it proves you correctly received your XMR. Note that a typical Monero transaction contains two outputs, of which one goes to the recipient (you) and one goes back to the sender as change. Intuitively, you can only "decrypt" the output that is going to you.

If you are using the GUI, you ought to perform the following steps:

Go to the Settings page of the GUI and press on Show seed & keys . Subsequently, copy the private / secret view key. Go to this tool, which was created by core-team member luigi1111. Furthermore, "Note: this site operates completely on client-side Javascript; no data is ever sent to the web server." Enter your transaction ID / hash in box 1. Transaction Hash: Enter your private / secret view key in box 2. Private Key Enter your public address in box 3. Recipient's Public Address: Press on Check . If it shows This address owns output x with pubkey: y for amount: z it proves you correctly received your XMR. Note that a typical Monero transaction contains two outputs, of which one goes to the recipient (you) and one goes back to the sender as change. Intuitively, you can only "decrypt" the output that is going to you.

If you are using the MyMonero, you ought to perform the following steps: