To improve programming skills, one should focus on problem solving, coding, design skills, and a eagerness to learn. It is important to learn from others by being open-minded, asking questions, and learning their thought processes. One should also learn how to work more effectively daily through writing clean code, using time well, and participating in code reviews and design discussions. It is also beneficial to learn the tools used everyday like Eclipse, IntelliJ, Git, Docker, and Linux commands to work more efficiently. Areas to focus on learning include trending technologies, and commonly used technologies like Kafka and Solr.