Changing from W7 to W10

> Model: WNDR3400v3|N600 Wireless Dual Band Router

   Is that accurate?  Firmware version?

> I've bought a new notebook with Windows 10. [...]

   Swell.  What is it?

> [...] My old computer with Windows 7 has genie on it. [...]

   Do you mean the Genie app for Windows?  Why not use a web browser?
Visit http://netgear.com/support , put in your model number, and look
for Documentation.  Get the User Manual.  Read.

> [...] I can't get to first base connecting with Windows 10. [...]

   What does that mean to you?  "can't" is not a useful problem
description.  It does not say what you did.  It does not say what
happened when you did it.  As usual, showing actual actions with their
actual results (error messages, LED indicators, ...) can be more helpful
than vague descriptions or interpretations.

   Are you trying to make a wireless-network connection to your router,
or what?

> [...] I've downloaded everything [...]

   What, exactly, does "everything" mean to you?

> [...] and tried to install Genie, [...]

   "tried"?  See "As usual, [...]", above.

> [...] but nothing seems to work on Windows 10.

   "nothing"?  "seems"?  See "As usual, [...]", above.

> How to I get Windows 10 to recognize and establish connection with my
> router? [...]

   By doing pretty much the same things as you would have done with
Windows 7.  Is there a wireless-network icon in your task bar?  If you
take your "a new notebook" to your local coffee shop, can you get it to
connect to _their_ router?  Does no one there run Windows 10?

> [...] Or is my router incompatable with Windows 10?

   No.