Hello and welcome to my User Tip
WiFi and Internet problems are hard to diagnose and usually rare, so this is my known list of possible causes /solutions seen here on the forums / experience
This is a work in progress, run through them and see if any of them work or apply to you.
On for some time, then just kicks one off / won't connect
You have a DCHP "lease" which allows a machine to be on a certain amount of time with the router.
Check the time and date are correct in your computers System Preferences and that it's being updated with Apple's time servers.
Check with Airport Utility that there is a update that needs to be applied to the Airport's firmware.
Also run your Software Update fully for OS X too.
Won't connect after wake from sleep, reboot, or coming back into range
If you have a "hidden network" it doesn't broadcast a SSID, the Mac will only ask if it's there upon a reboot or manual connection. Not upon a wake up from sleep or if it gets out of range of the Wifi.
To stop this you need to unhide your network, hidden networks and MAC address filtering offer no protection against hackers.
If that doesn't work, try this:
Go to your System Preference > Network > Airport > Advanced > Airport and use the "-" button to delete all your saved network connections.
Reboot the machine, and manually connect in the upper right hand corner and when it ask "save to keychain" do that.
Another way is to change your routers network name and/or security features, connect manually in the upper right hand corner and when it asks to save in KeyChain, do so.
New Mac or new location, won't connect
Newer Mac's are not connecting to WEP encrypted as it's basically worthless, WEP and WPA are both cracked only WPA2(AES) is secure.
Some ISP's are testing IPv6 and may cause issues, turn it off in your System Preferences > Network > Advanced > TCP / IP
Unplug, plug in your router or router/modem combo to reset it
Sometimes it's not your fault, it's the ISP having troubles, a loose connection, pulled wire outside or down the block, etc.
Bypass your router, connect directly to modem
Using a Ethernet cable, connect the Mac directly to the modem, power it on/off to get a new connection to the ISP and this way one can determine if the router is at fault or it's something further up the line.
Apple has some troubleshooting steps here too.
Secure your WIFI and privacy
Look at your Mac as a possible source of the problem
Sometimes the Mac is the problem due to corrupt caches (#12 OynX routine), a corrupt preference file (#12 OnyX > Verify > Preferences)
or it's the browser itself, try another and/or log into a new/anohter account to test.
Beware of those here recommending alternate DNS providers as a blanket solution
There are a group of regulars here, some of even high amount of points, that are shilling for OpenDNS or even GoogleDNS
They may provide IP addresses like 184.108.40.206 and 220.127.116.11 or 18.104.22.168 and 22.214.171.124 to enter into your Network Preferences > DNS settings as a cure all for you without discussing fully if it will resolve your issue or inquire about your Internet activity.
OpenDNS, GoogleDNS and others is a alternate Domain Name Server provider than the default one used by your Internet Service Provider when you set up your Mac or network
What this does is resolves domain names like www.apple.com into a IP address or number like 123.55.678.12 (not real) so your computer can connect to the site as that's how computers work.
You want to connect to Apple and the DNS provides the current IP address so your computer can connect.
It is done this way so Apple (and other sites) can change servers, IP's or locations and use the same name, much like a business keeps it's name but changes it's location.
Some are recommending alternate DNS as a solution to your problem when that's not in a lot of cases exactly what's causing your problems and in fact may bring more problems.
Sure ISP's DNS can have issues, so can OpenDNS or GoogleDNS. If you switch to alternate DNS you could have more long term problems than the short ones you possibly won't even resolve by doing so. Your ISP DNS is having issues and will be resolved shortly if you just wait some time.
OpenDNS does provide more protection against hostile web sites by default, blocking those sites from being accessed by your computer, with more (paid) content filtering as a paid log in option. Some see it as a benefit, but it can come at a painful cost.
Depending upon your location, using a alternate DNS can make your downloads much slower than before, especially Akamai/ISP based content which Apple uses a lot of, like for iTunes content and Software Updates, reinstalls of OS X 10.7/10.8+ for examples. This is because Akamai downloads goes by your DNS server location (not your actual location) to send the content from the closest ISP servers.
So using a alternate DNS can have a drastic effect on those who DNS server is located far away from the ISP server.
For instance it was discovered one of our top top regulars was experiencing problems with slow downloads, turned out he lived in Boston and the closest OpenDNS server was in NYC.
So when he went to download something, it always took a lot of time or had glitches, it's because his downloads were coming from NYC Akamai servers and when they were overloaded he was downloading from Chicago!
Soon as he switched his DNS settings back to his ISP's, his downloads speeds went back to normal.
Now if your ISP download server location is in say Miami for instance, and it also has a OpenDNS or GoogleDNS server, then there is no problem using a alternate DNS provider other than the fact that either one having problems will cause problems for you.
If you don't know what your doing, please leave the DNS settings alone.
If you don't do a whole lot of large content downloads, then you can certainly try a alternate DNS that has a server removed from your ISP's location, however the alternate DNS recommended to you may NOT be the fastest or the most stable it's all relative to your location.
You can use the free NameBench from Google to determine what is the fastest DNS. Enable the local DNS checks too, you might find out your local ISP DNS is indeed the best solution for your needs.
However give your ISP a fair shake, test a few times when they are not having issues so you can get a more accurate reading of their results.
You can certainly use a alternate DNS in the short term to troubleshoot your issue, if it's a ISP DNS issue or not.
Note that DNS settings need to be set on your router for all devices to use and on your computer if it's a portable model to use at other Internet locations.