to enter the web page of RE200, first of all, you should make sure your computer is connected to RE200, whether by wifi or by a cable though its Ethernet port. then you could use http://tplinkrepeater.net as the address in the address bar of your web browser.
if failed with domain name tplinkrepeater.net, then you may have a try to use the ip address 192.168.0.254. but some times the ip address of the repeater might change, you could check its ip address from the DHCP client list of your main router.

civic wrote

to enter the web page of RE200, first of all, you should make sure your computer is connected to RE200, whether by wifi or by a cable though its Ethernet port...

This is exactly my problem. The device won't connect to my computer through its wired Ethernet port (see original post). Wirelessly, either through its own wireless extention (which is working) or from the "back" through the router's wireless channel that it is extending, the Web-management page is inaccessible either by http://tplinkrepeater.net or by the address assigned by my router's DHCP (10.0.0.141). What other options are there?

I need more information about what can interfere with connection to the Ethernet port and/or with wireless access to the Web management page. - jclarkw

Details of OS and browser already provided.
HW version is V1.0
I cannot determine the SW version without access to the Web management page.

civic wrote

to enter the web page of RE200, first of all, you should make sure your computer is connected to RE200, whether by wifi or by a cable though its Ethernet port. then you could use http://tplinkrepeater.net as the address in the address bar of your web browser.
if failed with domain name tplinkrepeater.net, then you may have a try to use the ip address 192.168.0.254. but some times the ip address of the repeater might change, you could check its ip address from the DHCP client list of your main router.

I owe everyone an apology. I seem to have "locked myself out" of the Web-configuration page by permitting the wrong MAC address through the filter on my router. I'm still not clear on how this happened: the router told me that 84:16:F9:60:A4:61 was trying to connect, whereas the address printed on the back of the device was 84:16:F9:60:A4:60 -- only one digit different. Anyhow everything is working right now that I've permitted both MAC addresses, although I'm still not sure the first one is relevant.

Just in case it helps anyone else, here's what I've found out about accessing the Web-configuration page after the RE200 has already been set up. There appear to be only three options:

1) Wireless Connection: Disconnect the wired Ethernet cable. (It will no longer work, although see option 3 below.) Turn on wireless on the computer and select the extended wireless network (SSID) that was defined during setup. (This connection will require the password of the main router channel that the RE200 is extending.) Point the browser to tplinkrepeater.net and login using the new credentials defined during setup (changed login name and password).

2) Connection through Router (wired or wireless): Find the IP address assigned to the RE200 by the main router's DHCP, or assign a fixed IP address to the device during setup. (Note that this IP address is also available on the RE200's Status page if making the connection in step 1 but probably not during initial setup.) Point the browser to that IP address and login using the new credentials.

3) Direct Wired Connection (the hardest): First turn wireless off on the computer. Change the computer to a fixed IP address within the sub-net of the main router's LAN (in which the RE200 resides). Make a wired Ethernet connection between laptop and RE200. (It will show as having no Internet access, but that doesn't matter.) Point the browser to the IP address found in option 2 and login using the new credentials. After finished with the configuration page, don't forget to return the laptop to a DHCP-assigned IP address in order that it can get back on the router's network.

Best Regards to All. -- jclarkw