Refuse, reduce, reuse and then recycle.
Refuse to bring plastic into your home in the first place. Say no to straws, bags, wrapping etc where possible.
Switch to glass or aluminium/canned products where possible (eg pasta sauce?) as it's more efficiently recycled.
Switch to greengrocer or market if possible for fruit and veg, cuts out a lot of plastic. Carry paper bags/reusable cloth bags (I have a shopping kit in my car with all my containers, bags, Tupperware etc)
Reuse plastic containers if you can, before throwing out- so freeze meals in ice cream pots, use as plant pots for seedlings (will also reduce plastic use long term- we're going to grow our own salad leaves this year!) Use your old plastic pots to transport loose fruit/veg from the market etc.
Look at ecobricks if you would like to be involved in community projects to reduce plastic waste going to landfill
It's bloody hard to reduce plastic use with a busy family life. In 6 months we've probably reduced ours by 50% and I'd like to continue reducing. It's mostly been by switching brands, and specifically choosing brands based on their packaging. I've started home baking cakes/biscuits/savouries to reduce plastic on those things. It requires effort, time and sometimes money and there are times when I just can't afford the plastic free options.
I have noticed small changes in the last 6 months so hopefully there will be more changes on the way.