How do you....................?

Load all the weight over the front wheel (if it is a classic barrow, obviously - my mother had a weird two wheeled, long handled, low-slung device.), put little fingers over the end of the handles so you don't have to grip so hard, bend knees to lift it and use the body weight to get it going - and always start with the barrow pointing in the direction in which you're going to start pushing it.
Back in the day I was an archaeologist and being able to wheel a laden barrow along a wet plank without dropping it back into the trench was an essential skill. I guess health and safety has quite rightly demanded both a wider plank and some training these days ...

We once had some very innocent volunteers on a site who we convinced that barrows (the things you excavate) were so named because they usually contained barrows (the things you push along).