Although all the traditional steps in being chivalrous are all well and good, there may be other things that a modern girl is looking for. You could continue using the traditional methods of chivalry and add modern tenets to them.
In general, modern chivalry is going to be about respecting a woman. Call when you say you will. If you say you’re going to call on Friday evening, do it. If you can’t for some reason, then send an email or text message letting her know and when you can call.
Only make promises you can keep. If you can’t keep a promise, don’t make it in the first place. If you think you might be able to go out Friday night then say that you might be able to go. Don’t promise and then back out.
Let the woman know how you feel. Show signs of affection. Give her a kiss in public so she knows you want everyone to know she’s with you. Introduce her to your family and friends and make her feel special in general.
Do not disrespect the woman. Never say bad things about her to your friends. Keep these thoughts to yourself. If you have to, write in a personal journal.
Tell her how you feel and give things a chance to work out. If a problem arises, talk about it and try to work through it instead of just ending the relationship.
If the woman you are pursuing or dating is a feminist, you may even have more to consider about modern chivalry. This type of woman may not want the traditional chivalry but only the modern. She may want to split the cost of meals, showing that she is able to care for herself and that she’s not looking for anything from you. She may want you to be equals and make decisions together.
A modern woman may even want to pursue you once in a while. She may buy you flowers, or buy you dinner or a small gift. Take this to mean she likes you, and appreciate how far our society has come.