You get a sponsor by asking either durring a meeting or in person. You will get a lot of differant opinions but what worked for me was in the beginning I got a temporary sponsor who was more or less assigned to me. That relationship worked well for the first year. I then reached out to another man who I had come to know and deeply respected and he continues to be my sponsor.
My criteria for a sponsor is. They have been sober for a while 5+ years, they have worked the steps and continue to work the steps, they go to a lot of meetings, they are happy with life in general and compfortable in their own skin.
At the beginning I would talk about what you can expect of each other. Set some ground rules. Many sponsor sponsee relationships fail because of unrealistic expectations on both sides.
There is no time period but sooner is better than later.