Unable to login

> I received an email about a security download. [...]

   Netgear broadcasts such notices to all known users.  I wouldn't bet
that newer firmware is available for your (unspecified) "my router", but
it's worth a look.

> [...] "routerlogin.net" . I get a message stating I am not connected
> to my router's WiFi network. [...]

   Welcome to what may be the worst error message in the world.  For an
explanation, try:

      https://community.netgear.com/t5/x/x/m-p/1365830

   Briefly, the idea is that "[www.]routerlogin.net" (or ".com") should
point to your own router, but that's true only if you use your own
router for DNS name resolution.  Regardless, you should be able to get
to the thing using its IP address, if you can determine (or guess) that.
Normally, that would be something like "192.168.0.1" or "192.168.1.1",
but it could be different.

   It would also depend on what your (unspecified) "my router" is.

> [...] So how am I supposed to download the security update?

   Visit http://netgear.com/support , put in your model number, and look
for Downloads.  Under Firmware and Software Downloads, find the kit(s).
Download the kit you want.  Read the "Release Notes" file for
instructions.