The simplest way to create positive ions is usually to hit atoms with an electrical arc discharge. When the fast-moving electrons in the discharge hit the electrons in the atoms/molecules of matter, they knock other electrons 'out of orbit', which then head towards to positive anode. Leaving a positively charged, i.e. ionized, molecules.
This (Electrical Ioniziation, or IE) is known as a 'hard' ionizing technique. It tends to blast apart molecules. If you look up and read about mass spectrometry (MS), it's essentially all about ionizing molecules so they can then be sorted and detected according to weight. (their acceleration in an electric field will depend on charge and mass) So the area of MS has developed a bunch of different ionization methods for different molecules. E.g. MALDI for big biomolecules which would fragment into tiny pieces if blasted by an electrical arc.
As for what a cathode is, it depends on who you ask.
In most electrical contexts, it's the negative terminal. (I.e. defined as the more negatively charged end)
In electrochemical contexts, it's the positive terminal of a galvanic cell and the negative terminal of an electrolytical cell. The definition then is the end where chemical reduction occurs.
