I walk, I cycle or I use public transport.
I usually pick up groceries (for the next day or two) during my lunch break at work and then carry the bag home in the evening (which is really not a big deal). In the weekends I usually make one trip to the nearest mall to get some of the larger/heavier supplies I need. If I need really heavy stuff, I'll just have it delivered to my door.
I should probably note that the mall is 1.5 km from my house, the office 3 km. Obviously, if those are much further away in your situation, a car may be less optional for you.
Jim.