So happy to help: the more mother runners there are in the world, the better the world will be. Here are a few of my thoughts:
My biggest priority for beginning runners--yes, I get to have a priority for you--is to embrace the running lifestyle. I want you to be a lifelong runner, to want and need to run. So you have to make it a habit. For the first few weeks, make your priority simply to get out the door. Whether you go 1/2 a mile or 3; walk most of it or none of it; come home feeling elated or dejected, just go. Just like anything else worth doing, you have to practice moving when you'd rather stay prone in bed or on the couch. Eventually, it'll just become part of your routine and your body will expect it.
Not sure what you should do for the first few weeks? Oh, I have just the answer for you. Here's the 5K Finish It plan from Train Like a Mother. (It will open to a .pdf.) Along with the Half-Marathon Finish It plan, we're shelving this at the top of the site under Training Plans + Workouts, so you can access it whenever you need it.
Since we're talking about races, I'm a big believer in starting with a 5K, then progressing to a 10K or 5 miler, then jumping up to half-marathon, followed by marathon, if you're so inclined. By slowly bumping up your mileage and race distances, you'll help your body get used to the mileage and hopefully stay injury free. Crossing a marathon off a bucket list is certainly a worthy goal--and one I'll never discourage--but the marathon finish line will be that much sweeter if your body and mind are ready for it.
Join a group. We've got a plethora of women's clubs listed here. Reach out and tell them you're a beginning runner, and you'd love to find some newbies to run with too. I promise, you'll be so glad you did; running is so much easier--and more fun--with a buddy. If you don't have a club in your area, call a local running specialty store and see if they have a beginner class.
When you take on any race distance for the first time, the only goal should be to cross the finish line injury-free--and ideally, with a smile on your face. There is so much to learn and just experience by racing 3.1, 6.2, 13.1 and 26.2 for the first time; once you have a certain race distance under your soles, then you can get all crazy ambitious with your time goals.
Once you get rolling, there is no shame in walking. Yes, I know we're all runners, but sometimes a short break brings back your mojo. Limit the walk--one minute, to the top of the tough hill, to that mailbox, whatever--and then get your booty moving again.
Get out of the sprint mentality. Whatever notions you have of running being a empty-your-lungs-and-legs experience need to go out the window. You want to be able to talk when you run. If you're alone, try to recite the Star Spangled Banner or some Shakespeare or your grocery list. If you can only croak out one or two words, slow down.
One day, it'll feel easier. For some, that might be six weeks; for others, it could be six months. One day, your breathing will regulate itself into a nice little rhythm, and you'll look down at your watch and think, "Wow, I've already been running for 30 minutes! I feel so good!" Trust that it will come, and that it's worth every mile you put in until that point.
Even when it feels easier, not every run will be great. Or even good. But, as the cliche goes, you'll never regret a run you did--and the tough, blech runs just make the good runs feel amazing.
Those tips just scrape the tip of the iceberg: what are your best beginner tips?