If you're running OS X 10.8.4 or later, run Wireless Diagnostics and take the remedial steps suggested in the summary that appears, if any. The program also generates a large file of information about your system, which would be used by Apple Engineering in case of a support incident. Don't post the contents here.
If you're not using a wireless keyboard or trackpad, disable Bluetooth by selecting Turn Bluetooth Off from the menu with the Bluetooth icon. If you don't have that menu, open the Bluetooth preference pane in System Preferences and check the box marked Show Bluetooth in menu bar. Test. Continue if you find that Wi-Fi is faster with Bluetooth disabled.
From that same menu, select Open Bluetooth Preferences. If the box labeled Discoverable is checked, uncheck it. Click the Advanced button, and in the sheet that opens, uncheck the top three boxes, if any are checked. Click OK. Enable Bluetooth and test again.
If the application called "Bluetooth Setup Assistant" is running, quit it.
This step will erase all your settings in the Network preference pane. Make a note of them before you begin, and recreate them afterwards. It may be helpful to take screenshots of the preference pane.
Triple-click the line below on this page to select it:
Right-click or control-click the highlighted line and select
Services ▹ Reveal
from the contextual menu.* A folder should open with an item named "SystemConfiguration" selected. Move the selected item to the Trash. You may be prompted for your administrator password.
*If you don't see the contextual menu item, copy the selected text to the Clipboard (command-C). In the Finder, select
Go ▹ Go to Folder...
from the menu bar, paste into the box that opens (command-V). You won't see what you pasted because a line break is included. Press return.
Back up all data on the internal drive(s) before you hand over your computer to anyone. There are ways to back up a computer that isn't fully functional — ask if you need guidance.
If privacy is a concern, erase the data partition(s) with the option to write zeros* (do this only if you have at least two complete, independent backups, and you know how to restore to an empty drive from any of them.) Don’t erase the recovery partition, if present.