I have no practical experience either, but I'll share some good advice I've received.
First, know yourself and what you want. Part of that is serious reflection, but most of that is... dating. Don't automatically narrow yourself to one person or think that a conversation is the start of courtship. Just meet someone for coffee or a drink sometime... no big deal.
Maybe already have something in mind that you have in common to talk about, like travel, sports, fitness, or whatever. Again, no big deals about digging up family, children, headship, or heavy issues. If you can't click on simple conversation with somebody, how are you going to talk about a budget?
You eat lunch out during the week? Arrange to eat with someone. No big deal, you both will have to get back to work, so it won't turn painfully long. At least start with circulating so you can see what's out there, what they do/don't like about you, what is/isn't important to you.
As a nice guy, don't let the fear of "breaking up" stop you from starting something. You're past the teenage drama and the JW "dating is only for marriage". If it isn't working, both can and should come to terms with parting.
Good luck