Plastic free living is a huge overstatement right now. I use plastic every day, in all kinds of ways, though I've really cut back since I decided to give up single use plastics for Lent. I have lots of updates for you, but I'll start with food storage, since it's probably the easiest way to make a big impact in your day to day plastic consumption.
One big change has been eliminating plastic baggies and Ziploc containers from my lunches. I bought a stainless steel three-compartment tiffin for taking my lunch to work. So far it's been great, as long as I keep a bowl in my work desk to heat up hot meals.
Keep in mind: I ordered my tiffin from Amazon. That's obviously not ideal on an environmental scale either, but on a grad student schedule and budget, with no car, I'm limited in my shopping access.
Save pasta sauce jars and pickle jars to store food in in the fridge. When I studied abroad a few years ago, my friend and I did this out of necessity, but I never thought to do it once I returned home. You can even freeze food in these- just leave space for the food to expand.
The easiest-yet-hardest change is to use reusable grocery bags. Most people have them, and most people don't use them. I've been making a bigger effort, and I even made drawstring bags to take to the bulk bins at the grocery store- eliminating plastic packaging for things like rice or lentils. I've avoided produce bags altogether. I wash my apples and tomatoes when I get them home anyway, so that one-time-use produce bag isn't necessary. Keep in mind: I went to Whole Foods yesterday and they scolded me; apparently FDA regulations mean that you can't use a reusable bag at the bulk bins, though I've read of many bloggers doing this. You CAN use paper bags, though.
I'll admit it, I haven't been successful all across the board. Traveling, throwing a birthday party, and buying cheese are all terribly difficult to do without using loads of plastic- and I've done all those things in the past few weeks.
One reader asked if there's a good way to eliminate plastic garbage bags. While you can always reuse the plastic grocery bags most of us have jammed under the sink, those are too small to be ideal. If you really want to eliminate plastic bags, composting is probably the best option. Without wet food trash, you won't need a plastic garbage bag. Even apartment dwellers can start worm composting under their kitchen sinks, though I admit I'm not doing that just yet.
Despite these less-than-stellar moments, though, making these changes has only changed my standard of living in one way: I've been eating far healthier over the past few weeks. Eliminating plastic as much as possible also means eliminating most processed foods. The healthiest foods in the store- produce, grains, and beans, for example, don't come plastic wrapped.