I have a problem connecting to the internet.

Hello there!

It sounds like you are needing to power cycle your router whenever you login to your computer. The next time that it happens, before you restart the router to resolve, it use the wireless diagnostics available on Mac OS X 10.8.4 or later with this info from the following article:

Wi-Fi: How to troubleshoot Wi-Fi connectivity

Wi-Fi: How to troubleshoot Wi-Fi connectivity

OS X Mountain Lion v10.8.4 or later

Use the Wireless Diagnostics application included with OS X Mountain Lion v10.8.4 and later to identify and resolve Wi-Fi issues. For further information, please see About Wireless Diagnostics.

If you have 10.7 or earlier use these steps instead from the same article:

1. Make sure your software is up-to-date.
   
   • Install all software updates available for your Mac.
   • If you use a third-party Wi-Fi router, check with the manufacturer to confirm that it has the latest firmware installed. If an update is available, follow the manufacturer's instructions for updating the firmware.
   • To determine if your Apple Wi-Fi base station firmware is up-to-date, see Updating your software.
2. Check your connections.
   

   Some networking issues may be caused by loose or disconnected cables. Verify that all Ethernet and power cables connected between your modem and your Wi-Fi router are correct. Checking that devices such as your router and modem are on, disconnecting and carefully reconnecting Ethernet cables, and/or replacing damaged Ethernet cables may resolve the issue without any further troubleshooting.

3. Verify that you are using the recommended settings for your device.

See Recommended settings for Wi-Fi routers and access points.

And this section from toward the bottom if needed:

Symptom: The network connection drops unexpectedly

• Your Mac may not not stay connected to your Wi-Fi network reliably.
• Your Mac may stop accessing the Internet during use.

Thank you for using Apple Support Communities.

Cheers,

Sterling