Tip #1: Find where the photographer has past work publish
This might be on their own website, social media channels, or wedding directories such as wedding wire or the knot depending on where you live. It might even been on their local photography association. For me personally, you can find my past work in pretty much all of these places.
My top reason for this one is so that way you can not only see what their shooting style is, but also what their editing style is. To explain a little bit, their shooting style is how they pose or prompt their couples or if they shoot strictly candidly, and editing style is how they change the image post-session in order to create a final result.
Tip #2: Find how to contact them OUTSIDE OF THE DMS!!!
If the photographer that you are looking into takes their business seriously, they will have some form of contact form on their website, in their link in bio page, or will have a blurb somewhere saying to directly email or call them.
My personal preference with this is see if you can start a conversation with them in the DMs, but them move the conversation after some initial chat into some kind of email-based conversation. There is absolutely nothing wrong with initially connecting in the DMs, but once the initial conversation starters are through the photographer you're chatting with should direct you to fill out their contact form in order to start planning the session together.
To me, this just shows professionalism and that they operate as a business compared to just being a hobbyist. Nothing is saying they have to be full time in the business, but yet they still take all inquiries and sessions seriously.
Tip #3: Make sure their packages align with your timeline
I'm the first one to preach that every love story is different and so a copy + paste approach to wedding photography doesn't always work. A good photographer will offer a range of packages for whether you are looking at eloping, doing a small intimate ceremony, or you are wanting a full out bash with hundreds of people. While some photographers specialize in get one of those visions, they will be upfront about that. Some photographers like to stay to local venues and others like to do the destination thing only. Even within their specific areas, they will have different packages and customization options in order to create the best partnership with you.
I myself work with weddings of all sizes and locations. I have packages that range from only a couple of hours all the way to full day coverage with add ons and travel options available as well.
Regardless of who you choose to be your photographer for your BIG DAY, you have to know that you made the right choice and that you and them vibe together. It's your BIG DAY (and your babe's) so don't conform to how others think your day should go. There is literally a photographer out there for everyone and while I always hope that I'm the right one for a lot of people, I will also admit when I don't think I'm the right vendor for the inquiry. It's not often that I find that, but a professional knows what their specialities are and goes with it :)