Insert using PreparedStatement. How do I auto-increment the ID?

You should perform some modification(define default statement) to prepared statement string like this:

"INSERT into employee VALUES(default,?,?)"

That modification is because of occurring this problem : Column count doesn't match value count at row 1 JAVA mysql

After that you're code is something like below:

PreparedStatement preparedStatement = 
connect.prepareStatement("INSERT into employee VALUES (default,?,?)", Statement.RETURN_GENERATED_KEYS);

preparedStatement.setTimestamp(1, new java.sql.Timestamp(new java.util.Date().getTime()));                           
preparedStatement.setString(2, "Test");

preparedStatement.executeUpdate();

ResultSet tableKeys = preparedStatement.getGeneratedKeys();
tableKeys.next();

Thanks to Ic. for his answer.

Leave the column out of the INSERT statement entirely. It will be generated by the database engine. Your query should be:

INSERT INTO employee (time, name)
VALUES (?, ?)

Secondly, you have to perform the insert first, then get the keys out of the result.

I believe your code should be:

PreparedStatement preparedStatement = 
    connect.prepareStatement("INSERT into employee (time, name) VALUES (?,?)", 
    Statement.RETURN_GENERATED_KEYS);

preparedStatement.setTimestamp(1, 
    new java.sql.Timestamp(new java.util.Date().getTime()));                           
preparedStatement.setString(2, "Test");

preparedStatement.executeUpdate();

ResultSet tableKeys = preparedStatement.getGeneratedKeys();
tableKeys.next();
int autoGeneratedID = tableKeys.getInt(1);

Note this example does not check the success of the executed statement or the existence of returned keys.