How do I press charges for someone harassing us and slander on Internet

Is this person making false and defamatory statements about you or posting "personal" information about you that you do not want posted? I need additional information to understand exactly what is going on here. Defamation has certain requirements and you must prove that you suffered damages as a result of the "publication" of the false and defamatory statements to 3rd parties, in order to be awarded damages by a jury, unless your defamation is so bad that it is presumed that all persons would suffer damages from the defamation (lies that a person has a sexually transmittable disease, lies that claimant is a thief, etc are all defamation "per se"). These cases are filed in civil courts. You need to make sure you know exactly what you are filing and how to try a case, all rules of Texas Civil Procedure, the Texas Rules of Evidence, and Local Rules of Court. This would be nearly impossible for a layperson to do without the assistance and advice of an attorney. Go speak to an attorney and pay for an hour or two of their time before you go filing a lawsuit, "pro-se" (by yourself).

You asked about pressing charges. Criminal matters can only be handled by your local district attorney or US attorney. The first step would be to file a police report, then you would want to follow up with the DA. You can also file a civil complaint, but you could only recover money damages in that case, so if you are wanting this person to go to jail, that would have to be a case brought by a government entity.

As to pressing charges, you make a report to the police. The police will determine if there is enough to involve the prosecutor, who makes the decision. Harassment might qualify, but just doing something you do not like is not necessariy harassment. Slander (more likely libel), is grounds for a civil suit. For that, you hire a civil litigation attorney, whose first step will be to evaluate the strengh the case. Posting information, when true, is not defamation, and not a basis for suit. Posting pictures depends on where and how obtained. For that determination, you can consult your litigation attorney. When public information is posted, the poster may be doing nothing illegal or actionable, but sometimes sites will take down information on request. Your litigation attorney may also be able to advise you as to whether you have enough to file a police report.