So, Jan, here is the advise a good friend (who is female) offered me as I ventured back into the dating scene following a lengthy and nasty divorce:
First, be yourself. If you are typically outgoing and chatty, don't crawl into a shell. Engage the other person in conversation, find common grounds of interest. People's "BS" meters are always on in today's world, so no pretense.
Second, put your fears and anxieties aside. Dating norms are differed today than even a decade ago. It is perfectly normal and acceptable for a woman to suggest a causal meeting over coffee or lunch. Strangely, my friend stated that, if you are feeling some kind of connection, chances are the other person is as well.
Third, nothing ventured nothing gain. If it works out, great. If not, then no blood, no foul.
Not to make light of the situation, imagine how much fun you will have sharing your dating experience on this site.
In all seriousness, good luck and have fun.