"Buran" orbiters were assembled in Tushinskiy complex in Moscow (Тушинский авиастроительный завод). Than the orbiter articles were transported by VM-T airplane. The iconic An-225 was not ready in 1988.
MIK-112 in Baikonur was used for preflight/postflight maintenance.
( From Russian wikipedia
Производство орбитальных кораблей осуществлялось на Тушинском машиностроительном заводе с 1980 года; к 1984 году был готов первый полномасштабный экземпляр. С завода корабли доставлялись водным транспортом (на барже под тентом) в город Жуковский, а оттуда (с аэродрома Жуковский) — воздушным транспортом (на специальном самолёте-транспортировщике ВМ-Т) — на аэродром «Юбилейный» космодрома Байконур.
The production of orbital ships has been carried out at the Tushino Machine-Building Plant since 1980; by 1984, the first full-blown instance was ready. From the factory, ships were delivered by water (on a barge under cover) to the city of Zhukovsky near Moscow, and from there (from the Zhukovsky airfield) - by air (on a special BM-T carrier aircraft) to the Yubileiny aerodrome of the Baikonur Cosmodrome.
Here are couple of images of Buran assembly:
Energia rocket was too big, the parts were transported by air or by train and assembled in Baikonur.
Some details about Buran can be found also on site buran.ru (it has English version but it's some less detailed). I don't know how readable will be plain google translate of the Russian version...
Here is collection of photos of Buran and Energia rocket, including in-hangar photos, but not so high-resolution and with Russian captions.
Here is plogpost about ВТ-М cargo plane. (In Russian, but with many nice photos, including transporting Buran and Energia's conponents.) Photo from there:
Here a picture of loading of Buran on An-225:
Here are some photos of Buran installation to Energia rocket. You can see all operations were horizontal.
Here is video inside MIK-112 in Baikonur (in year 2017).
After second try I've found the real Klondike of Buran-Energia photos here!
The first photo there shows the crane parts for mating Buran to Energia:
I also found photo of Energia assembly with side boosters.