Starting lawn on a strip of weeds

I would like to extend my lawn a few feet and currently there are only weeds there, big dandelions, and other weeds. Don't worry I have lots of dandelions to replace those I want to get rid of and replace with lawn...

Any ideas on what would be best way to seed grass? I have never actually seeded a lawn before. Should I dig out all the weeds and then just apply seed or should I cover with newspaper, then bark, and then grass seed? I am not sure if the bark I had delivered for free is the right medium to lay over the newspaper either as most is rather chunky and not as fine as compost. If I dig out all the weeds, would I then apply compost over the top or bark? Not really sure what I am doing? This is only a strip of 3 feet by 15 feet long.

Thanks,
Beth

I wouldn't be doing it in the heat of summer but anyway....
I would take a garden rake and rough up the soil surface, whatever weeds get chewed up in the process is fine. Seed, walk all over to tamp the seed down, cover with a couple of inches of ground leaves or dry grass clippings. Moisten regularly.

You could just start mowing it along with your regular lawn. Over a period of time the grasses will take over and the weeds will be suppressed. Nothing wrong with a few dandelions in a lawn anyway.