When you include a string literal in a query, you can enclose the string in either single or double quotes; Access' database engine will accept either. So double quotes will avoid the problem with a string which contains a single quote.
SELECT * FROM tblStudents WHERE [name] Like "Daniel O'Neal";
If you want to keep the single quotes around your string, you can double up the single quote within it, as mentioned in other answers.
SELECT * FROM tblStudents WHERE [name] Like 'Daniel O''Neal';
Notice the square brackets surrounding name. I used the brackets to lessen the chance of confusing the database engine because name is a reserved word.
It's not clear why you're using the Like comparison in your query. Based on what you've shown, this should work instead.
SELECT * FROM tblStudents WHERE [name] = "Daniel O'Neal";