Where does "make install" put the files?

There is no rule but usually /usr/local (i.e., /usr/local/bin for binaries).

You can also specify where do you want to install with the --prefix option. For example

./configure --prefix /home/myuser

will install the software in your home directory.

Further to Matteo's answer, you can examine the Makefile to see where a particular program is going to install. Using GNU Hello as an example:

/usr/local/src/hello-2.10 $ cat Makefile | grep prefix
...
bindir = ${exec_prefix}/bin
datarootdir = ${prefix}/share
exec_prefix = ${prefix}
includedir = ${prefix}/include
libdir = ${exec_prefix}/lib
libexecdir = ${exec_prefix}/libexec
localstatedir = ${prefix}/var
prefix = /usr/local
...

We can see that this will be installed into /usr/local (the prefix variable). We can also see which subdirectories various files will be placed into, e.g., binaries (variable bindir)).

"make -n install" will do a dry run of the install process and tell you where things will be installed to.