What is the simplest way to remember por vs para?

Para points forwards: a goal, a purpose, a recipient, a deadline, a destination (estudio para ser médico - I study in order to become a doctor). Por points backwards or around: a cause, a reason, an exchange, a route, a means (lo hago por ti - I do it because of you / for your sake). If you can swap in 'in order to' or 'destined for', use para. If you can swap in 'because of', 'in exchange for' or 'through', use por.

Is it 'gracias por' or 'gracias para'?

Always gracias por. You thank someone for a reason or cause, and cause is por territory: gracias por la ayuda (thanks for the help), gracias por venir (thanks for coming). Gracias para is simply wrong. The same logic gives you perdón por and lo siento por.

Do you use por or para for time?

Both, for different time ideas. Por marks duration - how long something lasts: estudié por dos horas (I studied for two hours). Para marks a deadline - the point by which something must happen: lo necesito para el lunes (I need it by Monday). Duration is por, deadline is para.

Por vs Para

Both por and para translate as "for", which is why English speakers spend years guessing between them. Spanish does not see them as interchangeable at all. The split is clean once you stop translating and start thinking in terms of direction.

Para points forwards - to a goal, a purpose, a recipient, a destination, a deadline. It is the head of the arrow.

Por points backwards or sideways - to a cause, a motive, an exchange, a route, a means. It is everything behind and around the arrow.

Estudio para ser médico. (I study in order to become a doctor.) - the goal ahead.
Estudio por mi familia. (I study because of my family.) - the motive behind.

Hold that one contrast in your head and most cases resolve themselves.

The buckets for para (goal, destination, recipient)

Purpose / goal - "in order to", followed by an infinitive or a noun.

Vengo para hablar contigo. (I'm coming in order to talk to you.)
Es una crema para las manos. (It's a cream for the hands.)

Recipient - who or what something is destined for.

Este café es para ti. (This coffee is for you.)
Compré un regalo para mi madre. (I bought a present for my mother.)

Destination - where someone or something is headed.

Salgo para Madrid mañana. (I leave for Madrid tomorrow.)

Deadline - the point by which something must be done.

Lo necesito para el lunes. (I need it by Monday.)

Opinion / standard - "for", in the sense of "as far as ... is concerned".

Para mí, es la mejor ciudad. (For me, it's the best city.)
Para un niño, habla muy bien. (For a child, he speaks very well.)

The buckets for por (cause, exchange, route, means)

Cause / reason / motive - why something happens, who it is done for the sake of.

Lo hago por ti. (I do it for your sake / because of you.)
Gracias por la ayuda. (Thanks for the help.)
No fui por la lluvia. (I didn't go because of the rain.)

Exchange / price - one thing swapped for another.

Te doy diez euros por el libro. (I'll give you ten euros for the book.)
Cambié mi coche por uno nuevo. (I swapped my car for a new one.)

Duration - how long something lasts.

Viví en Madrid por tres años. (I lived in Madrid for three years.)

Movement through / along - the route, not the destination.

Caminamos por el parque. (We walked through the park.)
Pasé por tu calle. (I went along your street.)

Means / agent - by, by means of, by whom.

Te llamo por teléfono. (I'll call you by phone.)
El libro fue escrito por ella. (The book was written by her.)

Worked contrasts: where the swap changes the meaning

These minimal pairs are the heart of the topic. The sentence is grammatical either way; the meaning is different.

Lo hice por ti. = I did it because of you / for your sake (you were my motive). Lo hice para ti. = I did it for you (you are the recipient of the result).
Salgo para Madrid. = I'm leaving, heading to Madrid (destination). Salgo por Madrid. = I'm leaving via / around Madrid (route).
Trabajo para mi padre. = I work for my father (he's my employer - the goal of my work). Trabajo por mi padre. = I'm working in place of my father, or for his sake (substitution / motive).
Lo necesito para el lunes. = I need it by Monday (deadline). Lo necesito por el lunes. = clumsy, but reads as "I need it around Monday-ish" (approximate time).

A quick reference

Idea	Word	Example
Purpose / goal	para	Estudio para aprender.
Recipient	para	Es para ti.
Destination	para	Salgo para Madrid.
Deadline	para	Lo quiero para el lunes.
Opinion / standard	para	Para mí, es bueno.
Cause / motive	por	Lo hago por ti.
Exchange / price	por	Diez euros por el libro.
Duration	por	Estudié por dos horas.
Movement through / along	por	Caminé por el parque.
Means / agent	por	Te llamo por teléfono.

Common mistakes English speakers make

Using para to thank. It is always gracias por, never gracias para. Thanks point back at a cause, and cause is por.

Using para for duration. "I studied for two hours" tempts estudié para dos horas, but duration is por: estudié por dos horas. Reserve para for the deadline ("by when").

Using por for a destination. "I'm leaving for Madrid" tempts por, but a destination is para: salgo para Madrid. Use por only when you mean the route through somewhere.

Defaulting to one word for everything. The most damaging habit is picking a favourite and using it for every "for". They are not stylistic variants. Run the quick test: if "in order to" or "destined for" fits, it is para; if "because of", "in exchange for" or "through" fits, it is por.