I tried posting an answer last night, but it doesn't seem to have stuck.
A habit formed when gardening with chemicals is to spray when weeds turn up, but spraying something to control weeds isn't necessarily the best first choice, though there are a lot of organic sprays available. How you set up your garden is important to how many weeds you have later.
Once you've prepared the soil in the bed, try planting your bedding plants then surrounding them with a deep layer of mulch, or, what I do here, use a several-sheet deep overlapping layer of newspaper. Mulch over the top of the paper hides the paper and keeps moisture in, and will make it much harder for new weed seeds to germinate. When weeds do appear, if there seem to be more than are easy to pull, you can use 10% vinegar to spot spray (be careful not to hit the plants you want to keep. And do this on a warm day.)
In the turf, keeping it adequately fertilized will help the turf crowd out weeds, but the goal of an absolutely weed-free monoculture is harder to maintain. I'm not enamored of maintaining a lawn, I've been digging new beds and displacing lawn as fast as I can. (Bermuda grass is public enemy number one around here--it's so hard to keep out of adjacent beds if it is in the turf!)
I'd like to have clover in my lawn, like in the "old days" before the chemical pesticides were developed. Before then, no one was told that clover was a problem in a lawn. It's a way to market a new chemical, to create a new 'problem' for it to 'solve.'
Poke around through the library here for information about using vinegar spray (the March 12 weekly newsletter was all about using vinegar and types of vinegar). There is also a lot of good advice about establishing beds (everything from how to prepare, amend, mulch, etc. a dug bed to to pile up the materials and establish a "no-till" bed). And there are probably spotless lawns that are weed-free and totally organic, and people will have described how to achieve it.
Congratulations on making the shift to organic gardening. Give yourself a lot of time to read through this site--it is really a wealth of knowledge.