Easy. All you do is plug it in at work, and use the Alexa app on your phone. Go into Settings. Select your Echo, chose Update Wi-Fi and follow along. to connect to your work router. WHen you get home, do this again, but your home Wi-Fi will still be listed and you just switch to it, but then again, it likely will automagically connect to it, and when you take Fcho back to work, it will likely connect to it. Once you have registered a network it stays registered and you can go between them.
Hey, get a portable Tap or Dot to use at work. They go on sale from time to time it seems. I got a second Tap at 20% off last month. A Tap will join us on vacation next week.