A straightforward way to improving communication skills is through overcoming the main barriers to communication - be willing and be able to communicate.
A helpful start for improving communication skills is to analyze where in the process of communication most errors are made and to find out why. (We all have our strengths and weaknesses, as well as preferred styles of communication.)
Generally, being more open-minded and not fearful of new ideas is a big improvement - and there is always room for improvement here.
Improving communication skills through improving ableness works on two fronts: improving understanding of your own thoughts and expressing them clearly, and improving the comprehension of the words and thoughts of others (even and especially if their communication skills are lacking).
As with everything else - practice makes perfect.