The verb andar usually conveys meanings related to movement. Depending on the context, it can mean "to walk," "to work," or even "to ride." However, the verb andar is also used to talk about actions that are more often expressed with the verb estar (to be). Let's see how all this works.

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First, andar means "to walk":
 

Si tienes unas piernas fuertes y ganas de andar,

If you have some strong legs and feel like walking,

te lo recomiendo mucho.

I highly recommend it to you.

Captions 102-103, Blanca - Cómo moverse en Barcelona

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It can also be used to express movement, in which case it's better translated as "to go" or even "to ride":
 

Y por dondequiera que ando, tu recuerdo va conmigo.

And wherever I go, your memory goes with me.

Captions 16-17, El Ausente - Acto 1

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Yo ando en bici y tú andas en motocicleta.
I ride a bike and you ride a motorcycle.

When you use it to refer to the functioning of a machine or any sort of gadget, andar means "to work":

La lavadora no anda. | El carro anda bien. | La bicicleta no anda.
The washing machine doesn't work. | The car works well. | The bicycle doesn't work.

Spanish speakers also use the verb andar instead of the verb estar (to be). For example:
 

Me ha gustado, pues, el arte del circo, entonces por eso ando aquí.

I have liked, well, the circus arts, so that's why I'm here.

Caption 4, Circo Infantil de Nicaragua - Learning the Trade

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¿Dónde anduviste hoy?

Where have you been today?

Caption 9, Yago - 1 La llegada

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(Notice andar conjugates as tener (to have). Don't say "andé"!)

It can be used to express the state of being of a person, or an affair:
 

Tío, ¿qué pasa, hombre, cómo andas?

Pal, what's up, guy? How are you?

Caption 65, Animales en familia - La operación de Yaki

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Es que, bueno, las cosas, bueno... no andan bien.

The thing is that, well, things, well... are not going well.

Caption 21, Muñeca Brava - 8 Trampas

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Ando cansado. | Ella anda un poco triste últimamente.
I am tired. / I am feeling tired. | She has been a bit sad lately.

It is common to use andar for a state of being you have been feeling for some time and to use it with adverbs such as “lately” or “these days.”

Andar can replace estar when used as an auxiliary verb too:
 

Ando buscando un dormitorio más. (could also be: Estoy buscando un dormitorio más)

I'm looking for one more bedroom.

Caption 18, 75 minutos - Gangas para ricos - Part 12

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To say estar buscando and andar buscando is really the same. You hear Spanish speakers using them interchangeably all the time. If anything, using andar just adds a sense of vagueness or indetermination to the action. That's why it's commonly used to make estimations, for example:
 

Y ahora andarán sobre los, eh...

And now they would be about, um...

tres mil ochocientos, cuatro mil.

three thousand eight hundred, four thousand.

Captions 46-47, 75 minutos - Gangas para ricos - Part 13

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Here is another example:
 

¿Cómo explicarte lo que ando pensando? (could also be estoy pensando)

How to explain to you what I'm thinking?

Caption 2, Los Tetas - Como Quisiera Decirte

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So, while estoy pensando means "I'm thinking (right now)," ando pensando means "I'm thinking (right now but also maybe before that)." Again, in this context, both verbs mean exactly the same. 

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