Does 261A have the following equipment:
BT modem which has one USB socket
PC which has one RJ-45 Ethernet Socket and at least one USB socket
Laptop [LT] which has one RJ-45 Ethernet socket
The minimal scheme would then be to have PC communicate with the world through its USB connection to BT and have LT reach PC by Ethernet and then through PC to BT and the world.
What would need to be purchased would be one crossover RJ-45 EThernet cable to link LT to PC.
rotorcraig has given instructions on how to set up the PC and LT.
Simplicity would argue strongly against wireless in my opinion - since that would open up the can of worms about encryption and keys, workgroups, etc, etc, which 261A won't have to face with the simple crossover cable. Wireless without encryption will be unintentionally providing a neighbourhood WiFi hotspot. 261A can learn computer networking at a later date.
YMMV
seacue