Overlapping with information other posters have provided, especially @Richard Burts's posting, as described in the other postings, you'll need to make the inter-switch (and switch<>router) links (Cisco) trunks. (NB: trunk is a Cisco term, other vendors, such as Netgear may, or likely, use a different term [possibly "bundle"] for the same concept, i.e. an interface that can carry multiple VLANs. Also, a Cisco router defines a "trunk" interface differently from switches.)
An issue you may bump into, when mixing Cisco and non-Cisco equipment, Cisco allows for a "trunk" to carry one VLAN w/o tags, i.e. the "native" VLAN. Other vendors might not support this. If this is a problem, perhaps the easiest way to deal with it is to not use whatever is currently the "native" VLAN on the Cisco switches (by default, it's VLAN 1).
Cisco has a feature to selectively control what VLANs are allowed to use a trunk, but by default, they all should be allowed.
Another poster has mentioned VTP, a feature, generally, unique to Cisco. If using Netgear switches, and Cisco switches, perhaps best to disable on the Cisco switch. W/o it, you'll need to (manually) define all your VLANs on all your switches.
As Rick has mentioned, commonly, the way to block (or control) traffic between VLANs is with using interface ACLs on the L3 interfaces for those VLANs. Another possible way to do it would be to use VRFs (the L3 version of L2 VLANs), but that's a more complex approach.
