To add a new store, just tap the "Check-In" button on the main screen, then assuming the store you're looking for isn't listed on the next screen (within the chosen distance filter), tap the "Add New Store" button at the bottom.  

Then, tap the map where your new store is and a marker will appear, then select the retailer type from the blocks below, and finally put your store's full name, like "Asda Prospect Hill" in the name box and tap "Add Store", and you're done!  

If the shop is a small independent like a farm shop then you can select "Independent", or if the retailer is not on the list already, tap the "+" and you will be able to add them.