Shopping Online
One major benefit of doing your shopping online is having the ability to shop around. This could be a major cost-saver. Price comparison sites such as My Supermarket allow you to do your shopping through them, and show you the cost through each major grocery retailer. The results can be surprising, and may encourage you to switch.
This site also encourages you to swap for similar items which are cheaper - for example, from Heinz beans to Tesco's own. I would suggest that it's at least worth trying supermarket own brands. My husband was adamant he was "brand only"... but for a few months I slipped in "own brand" beans and he couldn't spot the difference! I eventually revealed what I'd done, and he was totally 'for' supermarket own brands in everything! Try it. You might just like it.
Do be careful though: I've found supermarket own brands aren't always the cheapest. This is where online shopping is great. Even if you go straight to the supermarket's site, you can search "baked beans" and it will show all of the results. Even if you search by aisle (which is the way I usually shop), the same products are likely to be next to each other, making it easy to find the cheapest brand. I have often found deals cheaper than supermarket own brands, or branded items the same price - so I've bought the brand.
Another thing you have to watch out for is the weight. In my early days of internet grocery shopping I bought a teeny weeny tube of toothpaste, thinking it was an ordinary sized one! After a while, you get used to the sizes. There are usually only one or two teeny weeny ones: the most common ones are the larger sizes. Looking at a product's weight also helps to determine if it's better buying a heavier item or two smaller items; for example, a 1kg tub of butter or 2 x 500g tubs. Again, sometimes the results may surprise you - especially when offers are on.
There are often vouchers available for shopping online. These may be for certain items (eg baby/toddler items at Asda) or for free delivery. I look online for them every time! A search in Google is all it takes. AND you can earn yourself cashback (if you haven't registered at Top Cashback or Quidco do so now!). It's money back on your shopping!
And all from the comfort of your sofa...
In store shopping
So, why bother even going in store?
Well, there are a couple of reasons... Some coupons can only be collected/redeemed in store. When there's a good offer on, or you have vouchers to redeem, it's worth the effort - even if it's just for a pint of milk.
You also don't have to pay for delivery charges. This may sound obvious but the supermarkets charge over the odds for delivery. If you do it yourself, you're making a saving there.
But the best reason? To follow the person round who is reducing all the items at the end of the day! Shops cannot sell food past their "sell by" date. This is different to the "use by" date, so you may get a couple of extra days. However, if you're willing to keep the items a few days past this date, you could grab yourself a bargain. The retailers are desperate to get rid of them - if they don't sell them, they'll have to chuck them - and so will reduce them to ridiculously low prices. You'll need to go to your local store about half an hour before closing (though the time does differ), find the person reducing them, and follow them to get the best deals. After a while you'll get used to the pattern (time, best day etc, usual person) and grab a basket full of bargains. Before you know it, you'll be showing off just what you got to all your friends!
So, my advice? Mix it up. Mostly online - in advance, to get a cheap delivery time. Then go grab the bargains in store!