Can you be more specific about your setup?
You say you have a LAN. Are you sure that you don't mean a USB modem plugged into phone socket and computer?
What is your computer? Is it a desktop or laptop. If the latter it will probably be wifi capable.
Assuming you have a simple modem/desktop or laptop setup, you will need:
1. Replace the modem with an ADSL+ Modem/Wireless Router. Go for the 802.11n 300x2 standard.
2. For the desktop get a suitable Network Card or a USB Network Adapter.
3. For the laptop either enable its wifi or get a USB adapter.
You may well find a 300n USB adapter is your best bet. In UK Maplin sell a Sitecom router and USB adapter for about £90