Hi there! I'm pretty tired and falling asleep for the night but I noticed your question and I worked on your exact model router for a client just a few hours ago so I'll see what I can do for you.
Basically a router gives out IP addresses [needed to access the internet] and gives one out to each computer in the network. Your incoming DSL connection gives you an external IP, and your router gives all your computers an Internal IP. 192.168.1.100 etc.
Your address for your router is 192.168.1.1, if it's still set at default, and I would say now is a safe time to reset your router. Locate the reset button on the back of your router and hold it in for about 15 seconds or so (you'll see your lights on the router change from their usual operation). This will allow us to continue from the beginning.
So, we're assuming now you have a wall jack, going to your modem, going to your trendnet routers "WAN" port. Now, you have one cable going to your desktop. From here, you have a wireless enabled laptop you'd like to connect. This is actually extremely simple.
All you need to do at this point is make sure you have access on your desktop by testing a page like www.google.com. If you see Google, you're ok! You have internet meaning the restarting of your router probably went just perfectly. The next step is to type in http://192.168.1.1 into your address bar. You will be presented with a login screen. This is the administration panel for your router. You're router has a built in web server to allow you to change these settings through a website interface nice and easily without having to do what most Network Administrators have to do and program it manually using a terminal connection.
From here, you can type in "admin" as your username, and "admin" as your password. If that fails to log you in, then just use "admin" as your username, and you should be in.
Now at this point, you can change your SSID (the name your router shows up as when you scan for wireless access points with your laptop) to whatever you like. For example "Wildimaginations". Click save, and you should see a very boring "Settings saved" screen with a back button. You're done! Go get your laptop and search for a wireless access point. If you don't know how to do that, post back here. You should see your newly configured router appear. You can double click on that, and accept that the router is insecure and continue anyways, and you're set.
If you want to secure your router a bit, I'll try to explain that best I can in my state. So assuming you've logged into your router using the previous instructions, you see the page for your router, you can head on over to the side navigation and select Wireless. You should be able to find "Security" in there somewhere. I'm way too tired to remember where it is, but one of the submenus of Wireless should be along the lines of security, and you can add a WPA password. Hopefully your router allows for WPA. I believe it does, if it uses WEP, then that's ok too. You can set a WEP passphrase, as they call it. Setting a WPA password is more secure, especially if the password contains numbers, letters, and odd characters like @$%$%. These are all accepted with a WPA password so you have lots of options to have a very secure password (up to 63 characters, making it near impossible for even a super computer to crack). All you have to do then is reconnect to the router from your laptop once the password is set, and it should prompt you for your new password.
Hope that helps!
