If an email is being blocked, then it will often show up on a blacklist, so users who suspect that their email is being blocked will want to first look at those blacklists. Emails coming from mail servers that have been blacklisted will often lead to some or all mail sent from that mail server not being delivered.
Another option is to create a second email account and to send an email from the account that may or may not be blocked to a second email. If it shows up then the person knows that their email isn't blocked, but if it doesn't show up, then the person knows that their email is blocked.
Before a person assumes that their email is blocked, however, they should give their emails time to arrive at their destination. Some email providers won't block email, but will delay it for hours or even days because they want to ensure that the email is legit. This process is called "graylisting." There are some email providers that claim not to use graylisting, but if the email header has a 450 temporary rejection error code, then the email address or the domain is being graylisted. The only way to change this is to contact the company responsible for the graylisting.