"Let's" and "Let"
I didn't see this question posted here when I searched so I'm posting it here.
I don't understand the phrase "let's" in Spanish. In English it's as simple as, "Let's do this" or "Let's not." There's no verb there. Like, to indicate what we're doing. My question is how do I form that? Like verbs that mean "Ya, let's do this!" (as in victory, or you want victory, or expect victory) or that mean "Uh, how about we not" (like let's not do this, it isn't a very good idea). Is there a shorthand for that like there is in English?
Also in Spanish, how do I say, "Let there be"? Like in the Bible, "Let there be rain, let there be light, etc." That kind of Biblical speak. Archaic but not really. Or "Let it happen," like you want it to happen and you hope it does, but you can't control it. I know the subjunctive is used here, but when I browsed the dictionary for this section it only came up with, "Por favor, que no llueva" which isn't what I'm looking for. I hope you can help me out.
Gracias.
3 Answers
Yes let and let us (let's) are difficult to translate into Spanish.
Here are a few sentences from my dictionary that may help you.
Let me think/see. / Déjame pensar/ver.
I wouldn’t let her. / No se lo permití.
Let the baby have the toy. / Déjale el juguete al niño.
Let there be no mistake. / Que quede bien claro.
My dad won’t let me smoke in my bedroom. / Mi padre no me deja fumar en mi habitación.
Let’s go! / ¡Vamos!
Let’s say…/ Pongamos por caso…
"Let it happen," / "Déjalo ser," (let it be)
I am not a native speaker - maybe one will come along and help you. 
Specific to your question about the Bible (Genesis 1:3) here is a link that has that Chapter in Spanish and you will see it is Sea la luz. The subjunctive form takes care of that expression. You will find as you study Spanish more that the Subjunctive in Spanish covers expressions in English that we say with extra words like: may, let, might, should, etc.
“Let’s “ can be conveyed in a number of ways. The easiest is to use “Vamos +a+ infinitive”
“¡Vamos a jugar al fútbol!”----Let’s play soccer.! “¡Vamos a comer!” Let’s eat! (my favorite. )
The other way is to use the “nosotros” form of the subjunctive. These same sentences would go like this:
“¡Juguemos al fútbol!” and “¡Comamos!
To say “let’s not!” There are several ways. “¡Mejor, no!( or "Mejor no lo hagamos." or even “Ummm, prefiero que no.” There are more but I can’t think of them all right now. This is enough to get you started.
In order to say "Let (something) happen" "Que sea luz." is Biblical, but "Que haya luz." is more modern.
"Let Joe do it!" "Que José lo haga."
To "let" in the sense of "allowing" someone to do something, use "permitir" as in one of the other answers, or even "dejar" "Voy a dejarle usar mi auto." I'm going to let him use my car.
This graphic is saying " Let's dance!"
