Hello! I´m Spanish and I can tell the difference between andar, caminar and pasear.

We use "caminar" when you walk with no reason, but in case you have it could be to do some exercise outdoors. Then, "pasear" means when you go for a walk but you are definitely looking for something and "andar" is similar to "caminar" but it is not as used as "caminar". It´s difficult to listen to someone saying "andar" at last in Uruguay.

Examples: Hagamos un poco de ejercicio" Que te parece si salimos a caminar de tarde? / Let's do some exercise! Why don't we go for a walk in the evening?

Vamos a pasear un poco, tenía ganas de ir al zoológico (one has a concrete place to go).

Hope it helps! 

The way I normally would use it is as follows:

Andar - take a stroll

Caminar - walk

Pasear - take a walk

Although short, hope this helps :)

When you say "let's go for a walk", in Spanish would be "vamos a pasear", that is, let's just wander around, kind of to enjoy nature, sightseeing, to breath fresh air, window shopping and such.  You employ the verb "pasear" like this as well: "Yo me paseo", "Tú te paseas", "Él/Ella se pasea", "Nosotros nos paseamos", either "Vosotros os paseáis" (Spain) or "Ustedes se pasean" (Latin America),  "Ellos/Ellas se pasean".

When you say "I walk to work", it means in Spanish "(yo) camino al trabajo".

"Andar" is more generic, kind of "moving".  "Yo me voy al trabajo andando" means "I go to work on foot";  "Yo ando en coche" means "I go by car".  One example of "andar" which we use very much in Southern South America: "Andate!" means: "Go!", and the person saying doesn't care which means of transportation you will use, just go!  It's not correct Spanish, though.  The correct word be "Vete!".  This is another example of usage of the verb "andar": "Andá vos!" (not correct Spanish), which means "don't try to fool me!", but it's always used in a friendly way, not meaning to be rude, very informal.