It's a lot easier to get appointed to a city, town or county board then you might think. Often times, public officials can't find good people to fill these positions. The fact one is a Libertarian hurts sometimes in getting an appointment, but many Libertarians have found that they can get an appointment anyway.
Search the internet for your town, city or county web site. Often it will have a site for one to apply for board positions, and the positions that are open.
Don't expect to get on the best boards. You won't. However, try to get on any board, learn the job, and do it well. Voters will notice how you apply Libertarian policies and how they work. Then, you will have a resume of success that you can apply to a future run for partisan office.
Here's an example of a web page from the city of Avon on openings on boards. Click here.