auslegen
to interpret
To interpret or understand something; to give something a particular meaning.
Man kann sein Schweigen als Zustimmung auslegen.
One can interpret his silence as agreement.

to interpret / lay out / advance
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to interpret
To interpret or understand something; to give something a particular meaning.
Man kann sein Schweigen als Zustimmung auslegen.
One can interpret his silence as agreement.

'Auslegen' (to interpret/to lay out/to advance money) is a separable verb. In a main clause, the prefix 'aus' goes at the end. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er legt die Dokumente für alle sichtbar aus.
He lays out the documents where everyone can see them.
The prefix 'aus-' often has the meaning 'outward' or 'to distribute'. This idea appears in many meanings: you put something out for viewing (spread it out), you put money out for others (advance it), or you put an interpretation outward (explain it).
Der Händler hat frisches Obst vor seinem Laden ausgelegt.
The vendor laid out fresh fruit in front of his shop.
If you want to say how something is interpreted, use the structure 'etwas als etwas auslegen' (to interpret something as something). The thing being interpreted is in the accusative.
Sein Lächeln wurde als Ironie ausgelegt.
His smile was interpreted as irony.
When you pay money for another person, use the structure 'etwas für jemanden auslegen' (to advance something for someone). The person is in the accusative after the preposition 'für'.
Keine Sorge, ich kann die Rechnung für dich auslegen.
Don't worry, I can advance the money for the bill for you.
When a surface is covered with a material, the preposition 'mit' (with) is used. The structure is: 'etwas mit etwas auslegen' (to cover something with something).
Wir haben das Kinderzimmer mit einem weichen Teppich ausgelegt.
We covered the children's room with a soft carpet.
In a technical context, the passive form 'auf etwas ausgelegt sein' (to be designed for something) is often used. The preposition 'auf' + accusative describes the purpose or property for which something was constructed.
Diese Maschine ist auf einen Dauerbetrieb von 24 Stunden ausgelegt.
This machine is designed for continuous 24-hour operation.
to explain / declare
'erklären' and 'auslegen' can both mean making something understandable. 'erklären' is the normal word when you tell someone how something works or what something means. 'auslegen' is more suitable when a text, a rule, or a statement can have several meanings and you choose a particular interpretation. The words can be confused because both occur with difficult texts. In practice: you explain a task or a device with 'erklären'. You interpret a law, a poem, or an unclear statement with 'auslegen'.

Die Gruppe legt den Satz im Text anders aus als die Lehrerin.
The group interprets the sentence in the text differently from the teacher.
Die Chefin hat dem neuen Mitarbeiter das Programm erklärt.
The boss explained the program to the new employee.