Prayer was the yardstick by which my wife and I each decided to marry. And I recommend it as the most important factor for faithful Latter-day Saints when considering such a decision. However, prayer comes in a lot of different flavors and qualities, and you'll only want the best for this endeavor!
A suitable prayer will involve studying it out in your mind beforehand. This probably involves dating for an extended period of time (none of this falling in love in two weeks flat that I've heard about!). You'll want to know how your partner reacts in a wide variety of circumstances and situations. You'll need to talk explicitly about financial philosophies, ideal family size, gender roles, commitment to the church. When a snag comes up, see whether and how you can deal with it together. The way you play off of each other, the way you can give and take, is really important since a good marriage requires a lot of that.
One "yardstick" I arbitrarily chose for myself was that my wife would need to make me want to be a better person. When my actual wife came along, I thought she failed that test since she didn't really give a flying flip whether I swore or watched R-rated movies. I thought, she doesn't care if I'm EVIL! But, she was fun to be with and look at, so I kept her around. ;-) Eventually I realized that in all the important ways, she does make me want to be a better person. Thanks to her support, I'm becoming the best doctor possible, the best father possible, the best husband, and even a more righteous person. Her patience and support has known no bounds. It's so humbling to think about that my gratitude actually makes me choked up just thinking about it. Anyway, I'm glad I didn't hold too tight to that one arbitrary yardstick (although some version of it is probably good).
There are a couple approaches I've seen recommended for making big decisions. One is to trust the intial flash of insight you get when you overall consider some complex issue. The research on this one is pretty interesting. Another approach is to do actual research yourself--to have the humility to consider that there's a lot of wisdom in the world that you can benefit from. For example, parenting is a scary thing, but it's been done before. If you want to be a good parent, one trick is to actually read a bit about what's worked well for others. You'd be amazed at the data easily available to people, and amazed at the scarcity of parents who give that data any regard.
In the case of marriage, there are gazillions of books available. In the case of mixed orientation marriage, there are some. In the case of LDS MOM, there are few. But, what advice exists ought to be appreciated. The higher the stakes, the more important it is to really be as informed as possible. However, each data point is only a data point. I'm not a fan of turning over life's most important decisions to "the authorities," but neither am I a fan of turning up one's nose at those authorities.
Taking one's mass of experience and information into consideration, one is more prepared to present the issue to the Lord. Even then, it may be hard to open the quality of communication desirable if one is out of the habit of praying or not keeping one's church covenants. Prayer's effectiveness falls outside of the realm of science to measure, in my opinion, and will depend on the faith and faithfulness of the individual (which can never be suitably quantified for comparison). The manual on prayer isn't a scientific one, it's the scriptures. And even more data can be had through the scriptures, so it's a good idea to make scripture reading a part of one's investigation too.
In my opinion, the most important decision I've made in my life was to marry my sweet wife. Left to my own doubts and second-guessing, I may not have done it. But I prayed about it and the answer was affirmative. Since God knows me better than I know myself, I got married. Now I believe my job is to never look back and to make all my thoughts and efforts focused on making it work rather than reconsidering indefinitely what I need or where I'll be happiest. It's one place I think the Savior's advice applies about finding your life through losing it. The results of my decision to marry, and my efforts to make it work, will have "infinite and eternal" ramifications. It makes me glad to think I trusted God.