One of the best things to do in order to make sure you remember to wash your new clothes "the right way" is to wash them right when you get home with them - even before you have worn them for the first time - as this will enable you to wash the clothes by themselves, without slipping up and forgetting.
If your new clothes have a lot of coloration in them (that is to say, if they have obviously been dyed), it will be especially important that you wash these clothes by themselves, which will keep this coloration from bleeding into your other clothes.
Clothes also have a tendency to either shrink funny or shrink a lot more than you wanted them to if you do not pay attention to the material; if your new clothes are made of cotton or wool, and are not listed as having been "pre-shrunk," you will want to wash them on cold water and dry them on low heat, which will allow the clothes to slowly tighten up and shrink just a bit, instead of shrinking a whole lot at once!
Once you have given these new clohtes two or three sets of washes on their own, it should be safe for you to add them to your regular loads - but make sure you do not add them before, lest you ruin some perfectly good clothes!