Ubud benefits from a tropical climate, and is slightly cooler than the coast as it's up in the mountains. There are two seasons: the rainy season and the dry season. Temperatures remain pretty high all year, and the rainy season is between December and January (the wettest month is January and the warmest month is October). Inevitably, the dry season can be the busiest, and although some tourists prefer not to visit in the rainy season, the rain quickly passes - so it all depends on what you'd prefer.
It takes around 1 hour to get from Denpasar Airport to Ubud, and there are plenty of taxi's available from the airport. Usually hotels, hostels and guesthouses will help you to arrange pickup so that you know that it's sorted before you get there - and they'll usually give you an already agreed price.