Buy tickets online – it doesn't save you money, but you can skip the queue, which can be a bonus during the busy periods (summer and major holidays). Also, be sure to check the weather forecast, because Swedish weather is notoriously volatile, at any time of year! And it's a good idea to browse the Skansen website ahead of your visit, to see what activities, performances, etc. are happening.
Skansen is a great place to experience any traditional celebrations and holidays, such as Midsummer, Walpurgis Night, Christmas, or New Year's Eve. But be aware that these days can often be the busiest times – meaning large crowds – as well.
The museum is open year round and has its charms in any season. However, admission is slightly lower during October, November and December.