Servir vs. verter vs. echar

The Spanish verbs 'servir', 'verter' and 'echar' can, among other things, all be translated as 'to pour', but they're typically used in different contexts and have different nuances.

Servir

'Servir' is generally used when referencing the act of serving a beverage or dish. It can denote both the physical act of pouring a drink and the larger action of serving a meal.
Me gusta servir el vino en estas copas.
(I like to pour the wine into these glasses.)
Voy a servir la sopa ahora. ¿Quieres un poco?
(I'm going to serve the soup now. Do you want some?)

Verter

'Verter' is usually used when you're pouring one substance into another. It typically implies that there's going to be a mixture between the two substances.
Debes verter el azúcar lentamente al batir los huevos.
(You should pour the sugar slowly while beating the eggs.)
Voy a verter un poco de leche en el café.
(I am going to pour some milk into the coffee.)

Echar

'Echar' generally indicates adding something to something else, often in smaller quantities than 'verter'. When used in context of pouring, it often suggests a more casual or careless action.
Él echó demasiado azúcar en su .
(He poured too much sugar in his tea.)
Si haces tortitas, echa un poco de mantequilla en la sartén primero.
(If you're making pancakes, pour a bit of butter in the pan first.)

Summary

While all three words loosely translate to 'pour', each has their own nuances: 'servir' relates most closely with serving food or beverages; 'verter' tends to imply a mixing or blending action; and 'echar', while also meaning ‘to pour’, indicates an addition of smaller quantities into something else and often carries a casual tone.