I'm looking for love for my mother-in-law. What's the best thing for me to do?
Last year, I answered this question  from "Foxy Senior," who was looking for love herself. I gave her several suggestions about local events to attend and organizations she could get involved with that were likely to cater to the kinds of people she wanted to meet. You could forward that post to your mother-in-law along with a non-threatening note like, "Thought you would find this interesting." If she doesn't have email, you could print it out and mail it or give it to her.
That's the extent of what I would suggest you do, though, without knowing whether or not your mother-in-law has expressed any interest in finding love. I'm curious about the context in which you either imagine or have solid evidence that she is looking for a relationship. Based on the way your question is phrased, I'm guessing you think that companionship would be good for her and have decided to be proactive. You may be right. However, meddling in the personal lives of one's elders, particularly one's mother-in-law, seems like the exact territory for which the phrase "treading lightly" was coined.
If you want to find a way to start a gentle conversation, say something like, "I've noticed that you've seemed kind of lonely lately. Have you thought about joining any seniors groups to try to make some new friends? I have some ideas if you're interested."
You both may be more comfortable approaching this from the standpoint of making friends rather than finding romance. You could also tell her about a specific event of interest and offer to attend with her. If you're especially close and especially bold, you could ask, "Have you though about getting back into the dating world?" Then listen to her answer and respond accordingly, rather than according to your own agenda.
If, in fact, she has reached out to you to let you know she's interested in dating, you can certainly be more direct. One option is to talk to your friends who have parents around the same age and find out if any of them know older gentlemen who might be up for an introduction. Direct her to any number of online dating sites geared towards seniors and offer to help her set up a profile. Once again, encourage her to attend local events and get involved with her community.
Be there as a sounding board, if she wants it, but don't try to micromanage her experiences. At the end of the day, or, at the end of the date, what really matters, regardless of your age, is feeling loved and supported by the people you already know.