Hello Jessie,
You should be able to find all the information you need concerning Google Places at the following URL.
http://www.google.com/support/places/?hl=en&rd=1
Getting listed in Google Places will require that you accept either of two verification methods:
1. Accept a verification phone call from Google via your business phone.
2. Request and return a verification post card via snail mail.
As for other free directories, I would recommend sticking to the larger well known directories such as yellowpages.com or dexknows.com and niche directories specific to your industry. Most directories online do very little to provide new leads or SEO benefits, and the more directory listings you create, the more listings you will be forced to maintain in the future when your business details change (think change of address, phone numbers, social media accounts, etc.).
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