Here is a list of idiomatic expressions using the word build.

Build fire under someone

This expression is used to refer to something that you do to force someone to start doing something.

The boss built a fire under his staff and they started working hard.

Build something over something / build something out over something

You can, for example, construct a bridge over a river. In this case it will extend over the river from one side to the other side.

We are planning to build a deck out over the pond.

Build upon something

When you build upon something you add to something you already have.

He built upon the success of his father.

Build someone/something up

To build somebody up is to make them stronger or bigger.

He has been advised to hit the gym to build up his muscles.

Build up can also mean promote or praise.

PR agents work hard to build up the reputation of their celebrity clients.

The media built him up into a visionary leader whom everybody expected to change the world.

Build someone up for something

To build someone up for something is to prepare them for.

They had to build her up before breaking the bad news.

Build something out of something

To build something using certain parts or materials

Children enjoy building towers out of the blocks.

Build something to order

To build something to order is to build it according to a set of specifications.

They got the car built to order.