First of all, the only way you'll ever be able to make sure a plot is "weed free" is if you pave it over, and the weeds will usually find a way in that case as well. I wouldn't worry too much about "weed free". The most important part is making sure that it's an area that's suitable for germination and growth for those seeds. That means good soil (good organics, not too rocky, not too much clay), enough light, enough water, and not too much competition from other plants.
And that last point is really what the "weed free" is referring to. You don't want something else germinating and growing faster than the seeds in your mix. Unfortunately, there's no simple answer to give on that, you'll have to keep an eye on it and try and figure out if some other plant is starting to take over your patch before the seed mix starts to grow. Pluck out things that don't belong there, or, at least, maybe thin out the things coming out so you have an even distribution (and the weeds will get lost in all the flowers).
One last thing I'd recommend is, as you're managing your patch of flowers, find the ones you like and/or the ones that grow well in your yard and save the seeds once their done flowering. Save the seeds for the next year. I find that far more fun than buying a new pack each year.