As far as I'm aware, there is no legislation specific to the co-option process, but all normal best practice rules must apply.
We publish a "job description" then invite applicants to submit a short written statement explaining how they will fulfil the role and what they'll bring to the table. Responses are circulated to members, then all applicants are invited to a Parish Council meeting, where members are given an opportunity to clarify anything that is unclear in the statements. We do not "interview" the candidates. We then conduct a written ballot, pass the voting papers to the Clerk, who collates the totals, passes them to the Chairman, who announces who the successful candidates are. We don't make public the number of votes cast, but this information is available to the candidates if they want it and, of course, to the public via FOI. With the whole process being conducted in an open and transparent manner, most people are satisfied with the result. It's also important for the Chairman to stress that future opportunities will arise and that unsuccessful candidates should re-apply.