A pre-emergent formula is one designed to protect lawns against weeds without killing grass. Apply these compounds before the weeds start to grow as an effective preventative measure and to remove the problems of dealing with full-grown weeds. Look for pre-emergent weed killers that are organic and biodegradable and then take a close look at ingredients to ensure it will only kill seeds and does not contain harsh chemicals.
There are also a number of weed killers that only kill a certain type of plant. For instance if you have a broadleaf weed problem, look for an organic weed killer that only targets broadleaf plants. Planet Natural has several targeted types of weed killers and you may be able to find eco-friendly or organic versions of many main brand solutions such as Weed Out.
Home remedies are tricky to use if you only want to spot-kill weeds. Vinegar and soap are common ingredients in these solutions. The vinegar is acidic and can make the soil inhospitable, while the soap covers leaves and roots to starve the weed. Salt and citrus oil are also commonly used. If you want to use these, apply them very sparingly only to the weeds, because they will often ruin nearby soil as well.
The best non-toxic way of getting rid of weeds while keeping your grass healthy may be to not use chemicals at all. If you have the time, using a trowel or pronged weed puller has many advantages. It allows you to get down to the root and remove the weed, it does not involve any harmful compounds, and it is immediately effective.