Why it's 'a foto' and 'o cinema': shortened nouns keep their gender
Portuguese loves short words. People rarely say fotografia or motocicleta in everyday speech. They say foto and moto. When a noun is shortened like this, it keeps the gender of the original long word, even if the new ending seems to point the other way. So foto and moto stay feminine, even though they end in -o, and cinema stays masculine, even though it ends in -a.
This catches English speakers because English nouns have no gender to remember. Learners who have just learnt the handy rule "-o is masculine, -a is feminine" apply it to these short words and end up saying o foto bonito instead of a foto bonita. The same goes for TV, mota and cinema.
Think of the short word as a nickname. It still refers to the same thing, so it keeps the same gender. Fotografia is feminine, so foto is feminine. Motocicleta is feminine, so moto is feminine. Everything that agrees with the noun follows suit: articles (a, uma), demonstratives (esta, essa), possessives (minha) and adjectives (bonita, nova).
The rule of thumb: when a word looks like a shortened form, ask yourself what the full word is and use its gender. The ending of the short form doesn't count.
The plural keeps the gender too: as fotos, as motos, as TVs.
Foto comes from fotografia, and moto comes from motocicleta. Both are feminine, so watch the adjectives.
In Portugal you will also hear mota. Here the ending happens to match, but it's the same feminine word.
TV is short for televisão, which is feminine. It stays feminine whether you mean the device in your living room or television as a medium.
Cinema works the other way round. It was originally a shortening of cinematógrafo, a masculine word, so it is o cinema, even though it ends in -a.
The typical mistake is letting the ending decide: o foto, um moto novo, a cinema. Correct forms are a foto, uma moto nova and o cinema.
Plenty of other shortened nouns keep their gender too, but they cause no trouble because the ending already fits. Examples are o quilo (from quilograma), o metro or o metrô (from metropolitano), o pneu (from pneumático) and o zoo.
A related habit is dropping the noun and keeping only the adjective. The gender then comes from the missing noun: o celular (o telefone celular), o portátil (o computador portátil), o micro-ondas (o forno micro-ondas) and a imobiliária (a agência imobiliária). The logic is the same: the hidden word sets the gender.
A shortened noun keeps the gender of the full word it comes from, whatever its new ending looks like. Say a foto, a moto, a mota and a TV because fotografia, motocicleta and televisão are feminine. Say o cinema because it goes back to the masculine cinematógrafo. Make every article and adjective agree with that original gender.