Ethernet was originally designed as a bus structure running over coaxial cable. THis means that all hosts saw all data. This also means that whenever a station wants to transmit, it is likely to come into conflict with another station. This is why Carrier Sense Multiple Access/Collision Detect (CSMA/CD) was invented and why it is used as the transmission method for most kinds of Ethernet.
To access the wire, the network interface card simply begins transmitting. If it detects that someone else is transmitting at the same time, that is called a collision. Both cards will detect the collision and stop transmitting. Each will wait a random ammount of time before transmitting again. Generally, this prevents conflicts over the network resources.
However, if there are too many stations on the local network segment, the number of collisions will rise and there will be no network resources for anyone. This is why it is usually a good idea to add switches to an Ethernet network.