I would say the best way is to build from the ground up. The strategy of "focus on the Presidential election" that the Libertarian and Green Parties have been using just doesn't work that well, since the main parties will always scream "Nader!" and "Perot!" in response, followed quickly by the standard "lesser of two evils" argument.
If they both focus on local elections--county seats, state reps, trustees, etc.--they can slowly build up not just their party organization in each state, but get voters more aware of just what the Libertarian Party and Green Party actually stand for--just what their ideologies are and how they might suit you better than the all encompassing Democrats or Republicans.
Then, when libertarian isn't just regarded as an internet meme about privatized roads and green isn't just a color, and there's serious organization and party affiliation, they can go after the big fish--the Senate, House, and Presidency.
Historically, it will be very difficult. Because of First Past The Post, our system is tailored for two parties, and a third party only really ever rises when one of the two main ones implodes. Perhaps someone will eventually come along to upend everything and get rid of FPTP--it isn't, after all, specified in the constitution what voting system shall be used to elect people--but given how entrenched politicians are, it would take someone truly extraordinary to implement a system that might cause their party to lose.
MadDoc The cutie said:
Now is not the time for a protest vote.
People wonder why Congress has a lower approval rating then root canals, why a majority don't trust both main candidates, why people hate it when politics is brought up in nonpolitical settings, why we have one of the lowest voter turn out rates--significantly lower than Botswana!
This is why. When people feel like they have to vote for a candidate they hate anyway because of some BS realpolitik excuse, they'll either opt out entirely, or grow to despise the very system and the people in it that they vote for.
If everyone voted for who they personally thought was the best candidate, I can guarantee the voting public wouldn't be so cynical and apathetic.