As mentioned, the Mishkan was made up of a number of boards that were connected through a series of sockets and pins; the roof was made of hides that were spread on top. Assembling something (and/or making a shelter) is building, the melacha of boneh.
While the av melacha (primary labor) involves both assembling separate pieces into a unified whole and forming a shelter, either activity is prohibited on Shabbos, even if the other is not accomplished. Accordingly, one may not pitch a tent or throw schach on the roof of a Succah (forming a shelter in the absence of assembling pieces). Likewise, one may not put together pre-fabricated furniture (such as one might get at Ikea), even though doing so does not create a shelter. Even screwing the handle into a broom is assembling and therefore boneh!
Home repairs are included under the melacha of boneh, as one is not permitted to add to an existing structure on Shabbos. Driving a nail into a wall for a picture hook or laying tile are adding to the building and therefore boneh. It is not boneh, however, when an action reflects an object’s normal mode of use. Therefore, if a sliding door comes off its track, it may be replaced. Similarly, one might replace the spring-operated dispenser that holds a roll of bathroom tissue. (This example is illustrative if not particularly practical, as bathroom tissue may not be torn on Shabbos, rendering the need to do this fairly moot. But you can replace the dispenser if you want to!)
While one may not assemble furniture or other utensils on Shabbos, one may open and close folding objects such as tables, chairs, portacribs and strollers. One may not use an umbrella on Shabbos, however, because it creates a shelter
Boneh has many details. This is a melacha that one may encounter many times each Shabbos without realizing it. Extra study in this area would therefore be appropriate.
This is just an introduction to the concepts of the melacha of boneh; it is not a substitute for a full study of the halachos.