Apple's menubar icon for Airport (802.11ac/b/g/n) Wireless looks like this either in blue or black and white, and if the lines are gray, it is not connected:
If the icon is just a black triangle outline of the shape of the blue lines, then it is turned off.
Clicking on it should usually help you find your wireless network, to connect to it, unless it already is secured and setup as a closed network that has not been configured before. Adding it to the preferred networks helps it automatically show up. Its own wireless routers are known as Airport base stations. 10.10.1 has some known issues with WiFi as far as what have been reported on the forum, so please compare notes with the possible solutions below.
Here are the most common reasons:
1. Updates can frequently cause the PRAM to need to be reset. Macs older than 4 years may need their
PRAM batteries replaced before this can be done. PRAM batteries are separate from the main power battery.
Some Macs only have a PRAM capacitor, and replacing that can be as expensive as a logicboard replacement.
2. People using WEP encryption or no encryption. WPA2 encryption is a must. That means no 802.11b
should be used at all, and any devices limited to Apple's original Airport standard should be hooked up via a WiFi/ethernet bridge using the ethernet side of the bridge. Extreme cards are compatible with 802.11g and WPA2.
Use these articles to determine which Airport card you are compatible with;
http://support.apple.com/kb/HT1621
http://support.apple.com/kb/HT3024
Intel Macs starting with Core2Duo and Xeon could have 802.11n internal cards added (or had them built-in), if not an 802.11g card upgraded to 802.11n with an inexpensive update from Apple. CoreDuo and CoreSolo Macs were limited 802.11g.
3. iCloud settings may be corrupted. Testing with iCloud turned off can confirm or deny this.
4. Same as #3 Software update settings may be corrupted.
5. The router used needs a firmware update to be compatible with the operating system in question. Sadly routers eventually get out of spec, and if their firmware is not updated they won't communicate well with a system that is newer.
6. 2.4 Ghz phones can interfere with wireless. Get 5.8 Ghz phones instead. Similarly if you are using 2.4 Ghz on other interfering devices, switching your wireless frequency to 5.8 Ghz can solve issues with interference.
7. A router has to be no closer than 3 feet (1 meter), or no further than 150 feet (50 meters) line of sight. Pipes and file cabinets can weaken the strength of the signal.
8. USB 3 can interfere with wireless. Try connecting only USB 2 devices to determine if you have one that is interfering with your wireless.
Look at http://www.everymac.com/ to determine if your Mac is USB 3 built-in, and you only have USB 3 devices, so you can determine if the problem is with the USB 3 device you have plugged in, or the USB 3 port that is there. Either the port may be damaged due to improper pulling or pushing cables (they must be done directly in and out, and not at any angle), or the USB 3 device may have a damaged cable or port.
9. Internet provider may not have a good domain nameserver. Using an OpenDNS can help.
10. Using a third party e-mail IMAP account, may need using a different port for sending messages, such as 2626, 2662, or 587.
11. Peer2peer software can slow down internet connections in general because they operate both directions, often when users don't expect them to.
12. At a WiFi hotspot, you can't get connected. The most frequent reason is the login screen for the WiFi hotspot is only able to be connected with a single type of browser. If Safari doesn't work, try Firefox, Chrome, Omniweb, or Opera.
13. Corporate WiFi networks in Mavericks (10.9) may experience timeouts. A solution has been posted to:
https://discussions.apple.com/thread/5483424
14. Disable Wake for network access on Apple menu -> System Preferences -> Energy Saver. This appears to solve the problem on 10.9.3 and certain 2013 iMacs, and maybe other Macs. Mac OS X 10.9.4 update mentions issues with Wake for network access are addressed to some degree.
15. If only certain websites don't work, it could be your antivirus software is too strong. Sophos has a web filter that can overdo itself.
Same problem with Little Snitch.
16. Proxy server settings are frequently used to optimize the speed with a specific internet service provider. Removing those settings lets you choose other DNS such as http://www.opendns.org/ which may be faster or less corrupted than your internet service provider's internet settings. Similarly, some internet providers support IPv4 better than IPv6. Apple offers settings to go either way. Apple offers PPPoE configuration options
in its networking hardware and software, but no PPPoA, some hardware offers on board settings to make those configurations for login that you can access via a router address using http://the router address/ though Apple's own Airport hardware has Apple Airport Admin or Airport Utility or configuration options through the Apple menu -> System Preferences -> Network.