Best way to contact a new business in order to give something for FREE?

Just be honest. I assume you're wanting to do it to build your portfolio? Tell them this. Perhaps as a lead in to offer them other services? Say you're hoping to show them what you can do, and would like to give them a free fan page to introduce them to other services you provide.

People still need a reason to be given stuff for free or they are sceptical. Up until now my offline career has been based on giving stuff away because I was terrible at sales. Let them know they are under no obligation and I feel people will appreciate you being straight up. That's how I always gave stuff away.

send an email or letter first. Then call to follow up on it and make your offer

Thank you for the advice.

You are right about people being skeptical when given "free" stuff. I just have to be honest with people like you are saying.

Cold calling can be difficult. There are people that do it well and it can be learned. I would suggest warming them up first. Try connecting with them through social media. Users of social media are going to be more likely to understand where you are coming from when you are talking about Facebook. I would suggest LinkedIn. I have heard of people having good success with "cold calling" there.

I tried giving away free online restaurant menus to restaurant owners in the past. I called hundreds of them, I read several books, studied website, and I could not get them to take the free offer. They were very skeptical. I believe this is because they have a lot of people contacting them all day long and they feel like everyone is just out to make a buck. I also believe it is because they didn't really understand the medium (the internet).

Another possible solution is to cross promote with a vendor they already do business with. For instance, let's say your target market gets water delivered every month. You could work with the water company to have their sales reps or drivers give your info to the businesses. Then, when you call, they will have already have heard about you.

I wouldn't waste my time with this.

The best way to do it would be to call and find out if they are experiencing any issues that your solution could fix.

By the time you've done that, you could have sold something rather than given it away.