To get the full path use:
readlink -f relative/path/to/file
To get the directory of a file:
dirname relative/path/to/file
You can also combine the two:
dirname $(readlink -f relative/path/to/file)
If readlink -f is not available on your system you can use this*:
function myreadlink() {
  (
  cd "$(dirname $1)"         # or  cd "${1%/*}"
  echo "$PWD/$(basename $1)" # or  echo "$PWD/${1##*/}"
  )
}
Note that if you only need to move to a directory of a file specified as a relative path, you don't need to know the absolute path, a relative path is perfectly legal, so just use:
cd $(dirname relative/path/to/file)
if you wish to go back (while the script is running) to the original path, use pushd instead of cd, and popd when you are done.
* While myreadlink above is good enough in the context of this question, it has some limitation relative to the readlink tool suggested above. For example it doesn't correctly follow a link to a file with different basename.