The right time to think about building your professional network - online and offline - is not at a critical life event, such as upon the loss of job or when transitioning from an academic institution. Networking should be a proactive part of professional practice.
Key questions to ask yourself when developing your network are:
How will I add value to my network relationships?
What are my goals?
In what channel(s) does it make the most sense to communicate to achieve results?
How do I best deliver my message (content form, factor, frequency)?
The most important quality that you need to maintain is authenticity. A transparent, genuine portrayal of your identity and intent will build trust. And as you blend your personal and professional networks, authenticity will afford you the opportunity to learn and evolve the ways in which you develop relationships and rapport, even if you misstep along the way.
To get started, consider who from personal, professional, and academic contexts you would like to maintain, or re-awaken, contact with. Like all relationships, networking requires interest by both parties in making the time required and continuing the care and feeding to deepen the connection. Most important to building trust and earning the right to keep in touch is reaching balance in the value equation. Ask yourself, "Am I building this relationship for my own gain, or do I have something to offer that is sincere and enduring?"
Networks that are built with the right intent will deliver results both in times of need and during the normal cadence of professional activities. As with most endeavors, intent counts more than technique, but mastering both will accelerate your ability to achieve results.