Tendering the suit to every possible carrier
Notify every insurer whose policy might respond, not just the one you think is most likely, and do it promptly in writing with a copy of the papers. General liability, professional liability, umbrella, directors and officers, and employment practices policies can each be relevant, and some require notice within a specific window. If you were working under a contract that made you an additional insured on someone else's policy, or that obliges another party to indemnify you, those parties and their insurers should receive the papers as well. Late notice can give an insurer grounds to contest coverage, so waiting to see whether the suit turns serious is a risk.
Reading the insurer's response
The insurer may accept the defense outright, accept it while reserving the right to deny coverage later, or decline. A reservation of rights letter deserves careful reading, because it identifies the issues the insurer may rely on later and can signal that its interests and yours have started to diverge. In some situations that divergence entitles you to counsel of your own choosing at the insurer's expense, and in others it does not. A denial is not necessarily the last word, and it can sometimes be challenged. Keep every coverage letter together with the date it arrived, since the timing of each response can matter later.
Working alongside defense counsel
Lawyers assigned by the insurer represent you, even though the insurer pays them, and you have a duty to cooperate with the defense. Keep your own records organized and share them through counsel, and avoid discussing the case with the plaintiff or posting about it. If the damages claimed exceed your policy limits, or parts of the claim fall outside coverage, you may want separate counsel to look after your uninsured exposure. Send us the complaint, your policies, any contracts that shift risk, and the insurer's letters, and we will sort out with you what needs to happen before the answer deadline.