how to get output of a script/program into a file?

The text that is displayed in the terminal comes from the stderr stream (2). If you do just make > build_log.txt, only the stdout (1) stream is redirected to the build_log.txt file.

• stdout is the standard output stream and has file descriptor number 1. This is the default stream being redirected in shells.
• stderr is the standard error stream and has file descriptor number 2

To redirect the stderr stream to that build_log.txt file too, use:

make > build_log.txt 2>&1

• make is executed and
  • the stdout stream is redirected (>) to build_log.txt
  • the stderr stream is redirected (2>) to the stdout stream (&1), which was redirected to build_log.txt

The order is important, you cannot switch switch the redirection operators like make 2>&1 > build_log.txt.

Alternative command:

make 2>&1 | tee build_log.txt > /dev/null

The redirection to /dev/null is needed to hide output, tee writes its input to build_log.txt and outputs it too.