Life is a (personal) journey.
Most people spend time working on themselves, exercising, getting in touch with friends/family members, reconnecting with hobbies and interests they may have neglected while married and eventually getting back out on the dating scene. Socializing is key.
Some folks join hobby/interest sites like Meetup.com and others go straight into online dating websites after doing some research.
Do whatever (you) feel like doing!
Every ending is a new beginning!