Hello isabeliain;
To connect to the internet with WiFi you don't need a phone.
Your Toshiba Satellite L510 probably has wireless capability built in.
For example this Toshiba Satellite L510-P402T Laptop has WiFi
http
/www.laptopspec.net/2009/08/toshiba-satellite-l510-p402t-14-inch-laptop/
Look under Specifications: Wireless Wi-Fi 802.11 B,G
With a WiFi laptop all you need in an access point/Hotspot/router and the password and you can connect to the internet.