How to Improve Signal Processing Skills?
One of the best ways is to hang out on this community.
Read questions and answers.
Try to replicate results on answers.

Once you have more knowledge, try answering questions of others.
If you encounter a question on a field you don't know, find resources to read about it until you can answer the question (Assuming it is not deep and requires deep knowledge).

Other classic approaches would be books.
Yet, I recommend Hand On approach.
Namely if you read a book, choose those which has code inside them to replicate results and have better understanding of real world models.

You may even look for some courses on Coursera:


Digital Signal Processing. 
Audio Signal Processing for Music Applications.
Fundamentals of Digital Image and Video Processing.


There are few options on edX as well:


Discrete Time Signal Processing.
Signals and Systems, Part 1.
Signals and Systems, Part 2.
Discrete Time Signals and Systems, Part 1: Time Domain.
Discrete Time Signals and Systems, Part 2: Frequency Domain.


For more classic recommendation you may refer to What Resources Are Recommended for an Introduction to Signal Processing (DSP)?

Enjoy the ride!