This is the nominal focus of conservatives' efforts to "secure the vote". Statistics concerning voter fraud indicate that it is extremely rare, but that efforts to combat it disenfranchise voters. Also, well-funded efforts to find evidence of voter fraud instead end up verifying it almost never occurs.
This is in part because impersonating other voters and waiting in line to vote in their place is a very time-consuming and risky way to manipulate elections. Other methods of getting government influence are much more cost-effective: political ads, voter suppression, gerrymandering, and lobbying, for example. But what are these risks? If caught, one impersonated vote can cost you up to five years in prison plus a fine of $10,000. The federal minimum wage of $7.25/hr means that five-year prison sentence effectively costs you at least another $14,500. For $24,500 you can run a 60-second ad visible to several hundred thousand eligible voters. Typically when voting, you need to show your name and address. (Details vary by state.) You must also vote in the correct precinct. If someone else uses the same combination of name, address, and precinct, they will commit the voter impersonation Kansan Kris Kobach is concerned about. (He was successful in making the voting process more restrictive, but not in proving the necessity of those restrictions: Since poll workers printed lists of who is eligible to vote, anyone who doesn't get the correct combination of name, address, and precinct will be denied the vote or be given a provisional ballot and further scrutiny.
Since poll workers maintain written records of who has come in to vote, duplicate votes will be recognized if the impersonated voter also casts their ballot: You can personally help prevent voter impersonation by voting, or by supporting the process as an election worker. Audits during or after vote-counting have the potential to detect various forms of fraud, including multiple ballots cast under the same name in different precincts, or ballots cast by people who should not have been able to vote.