It depends on what type of libertarian you are.
If you have only a mild case, you can sue based on the actual harm caused to you, which you would expect to have the economic damage done to you to be made good. You would have to show damage and reduced economic value to your property and the cost of any medical expenses cause by the pollution.
If you have a more severe case, you would need to agree with the other entity to enter into an arbitration, to determine if your claim has any merit. If it is a meritorious claim, the arbiter will recommend an award, which either the other party pays, or risks being seen as a bad actor. You may have the option of going to a loser pays court system, or not, depending on the severity of your libertarian infection.
If you have the most rabid form, then when you think that someone has done you harm, you hire the Mr. Guido protection agency, except that it is not really an agency because it is not really an incorporated business, because there is no central agency to grant corporate charters, while another private agency may grant charters, which really isn't an agency at all, unless some other private agency granted the agency the ability to issue charters, but I digress ... The idea being that who sign a contract with someone to enforce your rights, unless the other party fails to perform the contract, in which case you start over. Meanwhile, the other party has retained the services of the Whitefire security entity, which has subcontracted with some mercenaries, to ensure that the factory is not subject to inconvenience in conducting its operations. Now, the Mr. Guido agency and Whitefire, meet to discuss the matter, or decide to fight a proxy war on behalf of their clients, or decide that somebody's money is not worth the risk to their business. If you are not satisfied by the services provided by the Mr. Guido agency, then you can hire Bad Ass Special Forces Inc. (except that they are not a real corporation either) to redress your complaint against the Mr. Guido agency. I seem to have forgotten the original question.