To get free shipping from online stores, there are a few things you could try.
Firstly you could search online for a voucher code. Quite often popular stores will give away codes that can be entered at the checkout to get free shipping for that order. To find the code type the name of the store into a search engine, followed but 'free shipping code', and several websites may come up that will offer a code.
However the stores won't have codes available all the time, so it might be worth shopping around, or waiting a few weeks until the store you want has a voucher available.
Occasionally, an online store will be having a one day free shipping sale. It might help if you sign up to the stores email newsletter, then the site will alert you when these sales are taking place.
If you don't want to do this then keep checking the website, you might be luckily and happen to go on the site on one of the days where there is free postage.
If you really want free shipping then it could be worth ringing up the store and just asking. In some cases the shop would rather have your custom and give you free shipping, than losing you to another store.
Most sites that I have seen have a set price, that if you spend over, you get free shipping. For example if you spend over $50 in certain stores, then they will ship for free anyway. A site will usually give you the free shipping spending limit at the top of the page.
Big chain stores sometimes offer a click and collect service that gives free shipping. You buy what you want and they will deliver your items to your local branch, and you can pick your items up from there. Just make sure you don't end up spending more on petrol!