Once you have an identified case, you trace who they have been in close contact with recently and start contacting/testing/isolating them and trace it further from there
E.g. In Switzerland this was done manually (by medical staff mostly i think) in the very beginning, but they gave up very quickly on it because of lack of resources.
For context, Singapore has a team of 20 that can call contacts of confirmed cases, they are able to make 4000 calls a day. Those in contact with confirmed cases are made to a mandatory home quarantine, i think something like 35k people in Singapore are currently serving home quarantines.
As I understand, contact tracking is recording which people come into proximity so that if one gets sick the task of contact tracing can be facilitated by the contract tracking data.
E.g. In Switzerland this was done manually (by medical staff mostly i think) in the very beginning, but they gave up very quickly on it because of lack of resources.