The legal standard to bring a charge for impeachment is not even as high as a grand jury indictment. They can call anything "obstruction of justice" even if a court wouldn't consider it to be that. The only standard is that a majority of the House vote to approve the Article of Impeachment.
Then a trial takes place in the Senate. For POTUS the Constitution specifies that the Chief Justice shall preside over the trial. The "prosecutor", called House managers, present the case to the Senate. POTUS would have his own lawyers. Then the 2/3 majority is required to vote to convict/remove.
A successful impeachment/conviction causes a removal from office, there is no option to have any other penalty. The case can then be referred for prosecution through normal criminal procedure (where normal criminal penalties can be sought/obtained upon conviction).