Unfortunately, there is no easy way to check if someone received an email that you sent them. If you need to know an email has been received, the easiest way is to ask the person to reply to you when they get the email.
Some email programs include a "Return Receipt" feature, which adds the following header to an email message:
However, the presence of this header by itself will not necessarily trigger a return receipt. The recipient's email program must check for the presence of this header, and not all email programs do this. Additionally, the email program will often ask the user for confirmation before sending the return receipt, and the user may decline to send it.