There's a whole bundle of confusion in all of the posts above. Let's see if we can straighten it out:
Let's assume for the purposes of this review that you have just three devices on your network:
1. Router: provides access to internet and probably has both a number of ethernet ports and broadcasts a WiFi network.
2. Computer: Mac, Windows, or Linux. All access the network, and thence the internet, in essentially the same way, using either ethernet or WiFi connections.
3. Synology NAS box. Connected to the network using an ethernet cable.
The simplest way to set up the physical connections is to have an ethernet cable from both the computer and the Synology box to the router. You can optionally use a WiFi connection from the computer but with a server it is generally best to use a wired (ethernet) connection. Do not connect the computer and the server directly to each other - they must go through the router if you want them to have access to the internet.
Having physically connected the devices you need to configure them to be able to talk to each other.
This essentially requires that they all need to have unique IP addresses that are within the same subnet, that is an address that has the first three numbers the same (such as 192.168.1.x). The last number, indicated by the x, is a unique number for each device on the network which must be between 1 and 254.
You can either configure this setting manually, or connected devices can be set automatically by the router using the DHCP (Dynamic Host Configuration Protocol) server which is a fundamental element within it. The DHCP will give all connected computers which are set to use DHCP an address and other settings which are compatible with the subnet.
Just to cover the other aspects of the configuration, or if you want to take more control over the settings:
Router: self-explanatory - this is the IP address of the router. Another term for it is gateway, as it is the gateway to the internet.
Subnet Mask - this determines whether the computer can only talk to that subnet or can also talk to other subnets, but to avoid complexity (and because it is plenty for most domestic networks), it is best to use a subnet mask of 255.255.255.0 which is correct for all devices where the first three numbers of the IP address are the same. This enables them to talk to each other, provides for up to 254 devices on the subnet, and means that any attempts to connect to a device with an IP address which does not have the first three numbers the same will go out through the gateway to the internet.
DNS server - this is the device which converts an alphabetical address (such as
www.news.com) into an IP address (such as 123.123.123.123) which is the actual address used to communicate between devices on the network. This can be simply set to the same address as the router, which acts as a DNS server for the network. It buffers any DNS requests that are for destinations outside the local network, using an external DNS server to resolve them into their IP address on the internet.
Note that you can have both devices that are set up manually and devices that are set up by DHCP on the local network, as long as they don't end up with the same IP Address.
One quick thing to mention is that one of the devices above seems to have an IP address of 169.254.33.138. This is a special kind of address called a "self-assigned" address. The device which has this address has given itself this address because it cannot get an address any other way. It has not been able to connect to a DHCP server and in addition no-one has set it up manually.
Unfortunately a self-assigned address is pretty useless and will only work with other devices which have similar self-assigned addresses with the first two numbers the same. In most cases it is simply a warning sign that your network is not set up correctly.
I hope the above helps. It is a big subject and this is just a precis of the most important aspects of it.
