Step 1
Include the header in *.c file
include <sqlite3.h>
Step 2
Add the path of the header as C compiler argument -I
gcc -I/usr/local/include/sqlite3/ ...
Step 3
Add the path of the library file as compiler argument -L
gcc -L/usr/local/lib/sqlite3/ ...
Step 4
Add the library file as linker argument -l
gcc -lsqlite3 ...
It should now compile and work.