There is no One True Way™ to use an open-source C library. This article provides some guidance on how to use libbtc with various build/project tools.
libbtc is developed with autotools, and this will be the easiest way to build a binary from the source. Once you have autotools installed, performing a libbtc build is fairly simple.
$ ./autogen $ ./configure $ make $ make check
Once you have a build, you probably want to use it from within your application.
You'll need to include
btc/btc.h, and link to the binaries you built previously.