If you want something that appears as one network to devices and have portable devices be able to move between coverage areas very seamlessly, then what you are looking for is a set of devices that work together as a wireless mesh network. This is typically an option only found on higher end equipment. Usually from most of the name from brand name equipment providers. You cannot do this with the average consumer grade wireless devices (access points and/or range extenders).
My direct experience with wireless mesh networks have been from these enterprise types of equipment providers. It usually consists of a centralized controller that works in conjunction with however many wireless Access Points (AP) you need to get complete coverage over a given area. You must use the purpose built AP with these controllers and they are not usually interchangeable from vendor to vendor. You cannot use generic consumer level APs with a mesh controller. This is the type of solution that is used to provide wireless access over large areas or where the signal from one AP is not adequate. For example: hotels, stadiums, warehouses, auditoriums, corporate or educational campus, etc.
If you don't care that it looks like one network to any mobile roaming devices, then using multiple APs as suggested by the answer from @breakpoint is a good way to go for home use. The downsides are that some applications that want a constant connection may have some issues if you move from one wireless network to another. For example, streaming video may pause and stutter when you switch networks since the connection gets dropped on one AP and picked on on another. This is of course assuming or after your device is already configured to automatically re-associate with both/all of your APs.
Additional note: I mention this only as an aside, I have no first hand knowledge of or relationship to the following.... An associate used equipment from open-mesh.com which seems to be priced much lower than you typically see on enterprise level equipment and he seemingly had a good experience with it. Again, I have no direct first hand knowledge of this vendor but only mention it as most equipment you will find when you start searching will easily start well into the thousands of dollars range.