As gk90 said, the LIRR is the quickest way, but the subway-N22 is much cheaper.
There's a few N22 patterns.
* There's the regular N22, which makes all local stops, and takes Hillside-Willis-Jericho-Mineola, and then serves the Mineola Intermodal Center.
* There's the N22X, which runs AM rush from Jamaica, and PM rush back to Jamaica, and only serves the Mineola Intermodal Center. (So you'd have to make your way back to Willis from there)
* There's the N22A, which goes straight across Hillside (rush hour, both directions), and the closest it leaves you is by Hillside & Willis (so you'd have to walk down Willis from there)
* There's the N22L, which makes all N22 stops, except it bypasses the Mineola Intermodal Center (it runs both directions in the AM rush, and towards Hicksville in the PM rush)
It's a little confusing, but you should be able to figure it out. Basically, all N22s leave you within walking distance of Willis Avenue in Mineola. (If you give us an intersection, we can tell you which is the best N22 to take).
The schedule is
here.