The links below will take you to the main sources of information for public transport to and around Skye.
If you will be driving on the island, do read this. Distances and approximate times to reach Skye by road are here, and distances between places on the island are here.
"The preferred crossing for the discerning traveller..." Highly recommended. (summer only)
Scottish Citylink runs regular coach services between Skye and Glasgow (including Glasgow Airport) and between Skye and Inverness. Citylink coaches are also the way to travel within Skye along the main A87 road, from Kyleakin, through Broadford, Sligachan and Portree, to Uig.
The local bus and coach services here are operated by Stagecoach. You can download a timetable for their Skye services from here. Enter "Portree" into the box marked "Download bus timetable PDF". Clicking on any of the routes that come up will get you all the Skye bus times.
I'd give you a link direct to the bit you need, if only the good folk at Stagecoach would stop changing the URL every single time they issue a new timetable!
There are direct flights to Inverness Airport from Amsterdam and Dublin, and from a number of UK cities, including London, Manchester, Belfast, Birmingham and Bristol. Details do vary frequently, so it's best to check the latest information here.
Sing me a song of a dreamy moor,Where the maids at the shieling spin:Lull me to sleep by the peat fire smoor,When the soft night closes in.
Alasdair Alpin MacGregor