In short: You need to be as close to the router as possible, so put the router near to the center of your dwelling. If it is a three-story home or townhouse, try to put the router on the middle floor so that it can reach up and down as well as side to side.
Once you have your optimal location scoped out, look around for AC outlets and a way to bring the data to the router. If you can swing it, this is roughly where your router should be.
Admittedly, all this is often easier said than done. My house predates Wi-Fi by about 100 years and my cable data connection comes in at the north end of the house. Short of tearing up walls to bring the needed wiring to the middle of the structure, I need to keep my LAN gear on a shelf in the house's laundry room.
In order to keep the router near the center of your dwelling, you may have to make some adjustments. This equipment is on a shelf in the house's laundry room.
Something else to think about: Avoid setting up your router near a stone or brick wall; in addition, avoid large metallic items like file cabinets or refrigerators that can block the wireless signal. While the walls in my house are mostly made of plaster, which doesn't affect Wi-Fi as much, I also have some stone walls in the basement and the kitchen floor is made of concrete. All this diminishes the signal.
Setting up your router
There are three important setup tips that can smooth the transition to a new router -- all of which can be done in about a minute using the router's setup screens.
To get into the router's setup screens, you'll need to enter the router's base address (for example: 192.168.3.1) into a Web browser. You'll be asked for your name and password (which often defaults to something like "admin" and "password" -- you can usually find the information on one of the first pages in the manual).
I usually start by changing the base address of the new router to match the old one so that the change from the old to the new router will be invisible to any of my devices that connect to it. I also change the new router's range of IP addresses to match the old router's range for the same reason.
Next, it helps to make sure the SSID (service-set identifier) on the new router matches the one on the old router. This way, all your devices will recognize the new router as if nothing has changed.
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