Hire a bike at the entrance - the site is far too big to walk round comfortably
Take marshrutka 507 direct from Teremky metro. Pirogovo is an open-air museum of folk architecture founded in 1969, with over 300 buildings taken apart in villages across Ukraine and rebuilt here on the hillside. It's the same idea as Mamayeva Sloboda, which is closer to the centre, but on a completely different scale. Feofaniya runs from the same metro station if you'd rather have woodland than buildings.
That scale is the thing to plan around. The site is divided into sections, each given over to the folk architecture of a different region of the country, and walking the whole thing is a serious undertaking. Bikes can be hired, and unless you're a determined walker you'll want one.
What You'll See
The oldest and best known building is the Naddnipryanska church, built in 1742. Beyond that it's household after household - old textiles, carpets, costumes and ceramics, laid out as they would have been used rather than in glass cases.
The wooden windmills are the ones people photograph, and they're what most people remember. There are wooden workshops and shops too.
If you're interested in how people actually lived - the social and economic side of village life rather than the buildings alone - this is the best place in the country to see it. The museum city of Pereiaslav, about 90km out, has a third collection of the same sort if you get a taste for them.
Practical Notes
Guides are available and their English is good, so a tour is worth considering here in a way it isn't at every museum in Kyiv. Look out for the staff in traditional dress around the site, who will tell you about the buildings they're standing in.
The terrain rolls up and down and the air is a great deal fresher than in the city, which is half the appeal of a day out here. Bring decent shoes and plan on most of a day.