Whenever you need to buy anything for your home, a good place to look is for specialist stores of the category you are seeking, so the first port of call for any kind of lamps and light shades should probably be the specialist lighting stores in your area.
If you hit a blank with that, perhaps because your town is not awash with lighting stores, you can try any store which sells furniture or interior design items. The selection of lamp shades, especially if you are looking for a special kind such as square lamp shades, is likely to be limited but you may just strike lucky and find what you are looking for.
In any case, do not forget to look at discount retail stores and warehouses, which often have a selection of the latest designs at low prices, and if square lamp shades are in this season, then you might very well pick up a bargain.
Finally if you cannot get what you are looking for locally, take a look on the web. This would be the first port of call in terms of the sheer selection on offer and chances of finding what you need, but there is nothing like being able to see the goods and feel the quality before purchasing something especially when it comes to buying products for your home.
Sometimes, we imagine that a lamp shade will be just right but we have forgotten to take the actual measurements in the description into account. Or we think the color will be just right, but we forget that it is impossible to represent colors perfectly on a screen. Even so, you are likely to be able to get a good match between your requirements and what is on offer, and probably at a lower price too so it is worth buying lamp shades on the web if you are willing to return them if they are not quite right. Sometimes you can get something even better than you were expecting by taking a bit of a chance.