Once a notice of opposition is filed, the IP office notifies you and the registration process is paused. You will be given a set period to respond. The length of the response window varies by jurisdiction.
Most IP offices provide a cooling-off period at the start of opposition proceedings during which the parties can negotiate a settlement. Many oppositions are resolved at this stage through a co-existence agreement or other arrangement. If no settlement is reached, the proceedings enter an adversarial phase in which both parties submit arguments and evidence to the IP office, which then issues a decision.
If the opposition succeeds, the application is refused. If it fails, the application proceeds to registration. Either party can typically appeal the decision.