Major retail chains have "buyers" that choose what brands and products the stores carry. On their websites, you should be able to find contact info for their corporate offices. Call them up and ask for the appropriate buyer. You will specifically be looking for the buyer responsible for t-shirts. Sometimes, there are separate buyers for different regions. So you may want the Northwest buyer.
Try to make an appointment to meet with the buyer and show them samples of your brand. If you can't get an appointment (and don't be surprised if you can't), get an address to send linesheets and samples. You can also send a lookbook if you want.
If you want to sell through retailers, be prepared to need custom neck labels, hang tags, upc codes, etc.
Major retailers usually order in high volume, like thousands and maybe even tens of thousands of units. So make sure you are prepared to accept those types of orders. I know you are printing yourself, but you should consider outsourcing the production if you want to take on retail accounts like this. It's important to have consistent, high volume production capabilities to service big clients.
You will also have to extend payment terms, such as Net 30. And it's not uncommon for major retailers to require Net 90. This means you will have to pay all of the production costs up front and will not get paid until 30 (or 90) days after delivery.
Major retailers also sometimes require you to buy back any inventory that doesn't sell over a certain period of time.
Make sure you know your numbers... production costs, wholesale prices, suggested retail prices, minimum order quantities, timelines, etc. Pricing is a huge factor. Retailers want the highest profit margins they can get. So try to offer the best deal you can without sacrificing your own profit.