I have helped businesses with their Shopify sites for six years now and this question comes up quite frequently. Undoubtedly this is an issue facing many businesses, so here is some direction based on my experience.
Step 1: Consider whether free shipping works for your business
Pause for a moment and stop looking at it from a business perspective -- think of how you feel when you are a shopper. Customers would often rather pay more for a product, and get free shipping, than pay less for the product and pay for shipping. There seems to be something painful to customers about extra fees, shipping in particular. However, I've always said there really isn't any such thing as free shipping - the cost of it is usually factored into item pricing.
Step 2: Determine where to set your threshold for free shipping
From there, think of a few situations where you simply can't afford to offer free shipping. For example, for some lower-margin items, you couldn't afford to eat the cost of shipping if they are the only item in an order. This process gives you an idea of what your minimum threshold for free shipping needs to be. Oftentimes that pricepoint is $100 but if you sell something like pencils that might be too high, LOL.
Another consideration for setting your free-shipping threshold is your average item price. Ideally, you want orders to contain more than one item so consider setting the threshold at a price that would require more than one item to be in the cart. For example, if your average item price is $50, you'd want your free shipping threshold to be $65 so that it encourages people to buy multiple items.
Step 3: Decide how much to charge for shipping when it's necessary
Go into a post office or a UPS store and work with them to get ideas on how much shipping to various areas will cost, using the actual weight and size of your products with packaging. You need to know these figures before you make any decisions. In Shopify, you can set different free shipping thresholds for different areas. For example, free shipping in Alberta on orders over $30 and free shipping Canada-wide on orders over $100 could be options, with a $5 flat-rate for orders not meeting these criteria. Whatever you decide, be sure to clearly communicate your rates to your customers so they are not surprised at the checkout - this can be a huge deterrent to a converting customers into sales.
Step 4: Monitor and Adjust
Lastly, remember you can always make changes after awhile – nothing is set in stone. If you look at a month of sales and feel like you are charging too much or too little, make adjustments. If you're charging for shipping and seeing a large number of abandoned carts, that could be a clue that your rates are too high. I find this is an area where businesses tend to think they need to get it perfect, and that can be pretty overwhelming. Take the pressure off yourself and work with the numbers to find the balance for your business and customers.
Once you've decided on your Shipping rates, if you need guidance on how to actually set them in in Shopify, check out this tutorial -- you'll be up and running in no time.