PLEASE NOTE that climbing this mountain can be very dangerous. It is not a walk and demands scrambling.
Isle of Skye, also known as "Misty Isle", has only few really good days for climbing the higher mountains. The best time is usually from mid April to the end of May, but you can be lucky and experience a great day throughout the whole year. From my experience, it is better to start after noon, since evenings are usually more calm on Skye. Check the forecast before you go! Note that climbing Sgurr Alasdair requires mountain experience. People who suffer from vertigo should not try this. Note that Cuillin ridge can be very dangerous place for people who underestimate it. Weather can change very quickly and navigation is very hard on the ridge. Use proper clothes, shoes and equipment when going to the ridge and be ready for every eventuality.