Fortunately life as an artist is a bit easier these days as compared to when I began more than 10 years ago. At that time I had to travel more to research venues as well as prepare and mail out an artist's package complete with slides of my work along with print material, and now most of it can be done digitally.
Regardless, I still follow the same steps as I did before, though now the cost and time requirement have decreased substantially.
1. Do your research...find out if this a good fit for you & your work and if it will be a pleasure or a challenge to be involved in this particular manner. If there is other work in the gallery or public space or magazine, view it. Make sure your work is different but not totally (ie. don't submit paintings to a gallery that only represents prints) and feels like it would belong.
2. Prepare a resume which includes any work that is related or relevant to the project/submission. This includes exhibits and any art-related work such as volunteering.
3. Create a portfolio page of 10-20 images relevant to the submission. Your images should be clear and the colour accurate.
4. Write a cover letter in your own words that briefly introduces you and what you do and why you'd love to be involved.
5. And, what I believe to be the most important...MAKE SURE YOU LOVE IT. Trust your gut. I have learned to make a point of only being involved in something I would do in spite of any recognition or sales. That way, I won't be disappointed.
Often a website link is all that is required so be sure to keep your own website current, typo-free and authentic to you. It helps to have a second pair of eyes preview what you've written and uploaded. It also helps to take a peek at how other artists present themselves and select what suits you.