You can see your Mac's currently assigned private/local IP Address in the Network Preference pane:
Because this system is connected to a router, the system's assigned IP Address, Subnet Mask, and Router address are visible in the display. Make a note of these.
When we assign a static IP address, we want to assign one that meets two important criteria:
To make sure your Mac's IP Address stays the same, change your Network Preferences configuration, on the TCP/IP tab, by changing the Configure pull-down menu to say Manually. Then you need to enter the IP Address, Subnet Mask, and Router Address for your network. The Subnet Mask and Router address you fill in should stay the same as they values that were dynamically assigned when you were using DHCP (see above.) Also fill in your ISP's Domain Name Server (DNS) information (It should be part of the setup information they gave you. If you don't have that for some reason, you can often just use the Router's IP Address - e.g. 192.168.1.1 for the LinkSys; the router should have obtained the DNS info via DHCP or PPPoE from your ISP.)
In this example, I chose 192.168.1.20 for my Server's IP Address. That address works well with a LinkSys router: It's on the same sub-network as the LinkSys (192.168.1.--). I haven't used it for any other computer I have. And, the LinkSys DHCP server assigns IP addresses starting with 192.168.1.100, so it won't duplicate that address, either.
You can usually check which IP addresses your router's DHCP server assigns to the computers on its LAN with it's configuration utility. E.g., with the LinkSys, you can check it on the DHCP tab ("Starting IP Address"):
That's the default setting for a LinkSys. I've seen no good reason to change it.
With Apple's Airport Base Station, you can see the DHCP range it assigns on the Airport Admin Utility's Network tab ("Beginning", "Ending").
The Airport base station uses addresses that start 10.0.1.*, starting at 10.0.1.2 (10.0.1.1 is the Airport itself.) That's the default setting for an Airport Base Station. I've seen no good reason to change it. So, with an Airport, I suggest using an IP address such as 10.0.1.220 for your manually-assigned IP Address. (With 255.255.255.0 for the subnet mask and 10.0.1.1 for the router address; use 10.0.1.1 for the DNS server if you don't have the exact Name Server/DNS address(es) the ISP assigned.)
Each router brand seems to have its own default DHCP settings for allocating IP addresses on the LAN. You need to pick an IP address on the same sub-network as the others, but not in the range DHCP will allocate. The table below shows the default DHCP setup for several popular router brands:
Router Brand Default Router Address Default DHCP-assigned IP Addresses Sugested Manually-assigned IP Addresses Apple Extreme Airport Base Station 192.168.1.1 192.168.1.2 - 192.168.1.199 192.168.1.201, 192.168.1.202,... Apple Airport Base Station 10.0.1.1 10.0.1.2 - 10.0.1.100 10.0.1.201, 10.0.1.202,... LinkSys 192.168.1.1 192.168.1.100 - 192.168.1.199 192.168.1.10, 192.168.1.11,... DLink 192.168.0.1 192.168.0.100 - 192.168.0.199 192.168.0.10, 192.168.0.11,... Belkin 192.168.2.1 192.168.2.2 - 192.168.2.100 192.168.2.201, 192.168.2.202,.... NetGear 192.168.0.1 192.168.0.2 - 192.168.0.50 192.168.0.201, 192.168.0.202,...
Remember not to give the same number to more than one computer in your network!
After you've assigned your Mac a static IP address, it should still be able to connect through your router to the internet. This would be a good time to check that nothing's gone wrong by trying that.
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