One way to save at ASOS is by simply being patient. "Saving" those full-priced items that interest you and then revisiting them when there is a sitewide sale or ASOS discount code, is an easy way to get a discount on all products, whether they are high-end or just a little outside of what you're willing to pay.
ASOS will keep your "Saved" items for up to six months. After those six months, your items will expire. Take note, that once specific items are discounted, they tend to sell out quickly. So, be sure to keep an eye on those must-have items that you've saved, either in the app or logged in online, before they expire from your saved list or sell out!