There are several things you can do if you can't get connected to your WiFi hotpot or router.
1). Some channels work better than others. 1 and 6 are popular and work well for many people. If you can get connected at all, download WiFi Analyzer This app will give you an idea what channels may be available or over lapping with a nearby router. It will also display signal strength.
2). Restart your router. This sounds simple but has been the solution for many people. Routers frequently accumulate garbage in the system that can be dumped by removing the power cord for at least 30 seconds then plugging it back in. After the router has made a connection, restart your TF You also should check to see if there is a firmware update for the router. That could make all the difference. In a few cases some people just replaced an really old router and ended up really happy they did.
3). As is the case with some other devices, the TF doesn't do a great job of telling you there is an error when inputting your password or passphrase. If the TF says it is trying to connect for more than 10-15 seconds you may have mistyped the required information. Long press the connection and tell it to forget your credentials and try again. If your TF at some point says saved but you are obviously not connected, you may have a poor signal from the router or you are too far away, or there is other interference or it can also happen at times if can't authenticate with the router correctly. You can also try turning the WiFi off then back on again.
4). I have found that the TF does not work well or at all with WEP encryption on some routers so your best bet is to use WPA/WPA2 or equivalent. If possible do not set it to WPA/WPA2 mixed mode is it still isn't working. This is better security than WEP anyway. If you still can't connect but see a strong signal try no encryption long enough to determine that it is possible to connect and adjust accordingly. It also may help, in combination with WPA/WPA2 to use TKIP rather than AES encryption.
5). In order to narrow the problem down, if all else is failing, try connecting to a public hotspot or a friend's router.
6) If 1-5 don't help, do a cold start, (aka hard reset), of the TF. With the TF turned off, hold the volume button in the down position and while holding the volume button hold the power button. Hold both until you clearly see some white text in the upper left corner of the screen then let go of both buttons. You should then see 2 icons, (4 on Jelly Bean), on the screen with the one on the right flashing on ICS and the one on the left on JB. Wait until the TF restarts. Note, double check all your settings as this can causes one or 2 minor changes, like screen timeouts for instance. (note: you may not see the 2, or 4, icons if you are rooted but it will still accomplish the same thing).
There are some things you can do to improve your WiFi. Cordless phones typically operate at 2.4 GHz, so does the TF. Keep cordless phones as far away as possible from your WiFi router. Same applies to a microwave oven.
There are repeaters available. The best ones would be the same brand as the router but others work. ASUS has a portable router that can act as a repeater/extender for just about any router, model WL-330N3G. This mobile wireless router will also work with select 3G dongles.
There are 2 parts to an Internet connection.
Part 1 - the WiFi connection between the tablet and router.
Part 2 - the connection between the router and the Internet.
There have been users who have an issue with part 1 (wifi) on their tablet, but the same wifi connection they have on another device works fine and their tablet will not connect to anything and has a grey wifi icon.
In this case, it has nothing to do with the speed if the internet connection because other devices are working on w wifi and the tablet is not.
In many cases their wifi router is not shaking hands properly and a simple reboot of the WiFi router fixes the issue, and had nothing to do with the type if Internet connection.
These instructions work for all Transformer models