Most two-part conjunctions in German have direct English equivalents, so it's faster to learn them by example than to break them down grammatically. The easiest are either/or and neither/nor:

Wir können entweder ins Kino oder ins Restaurant gehen.
We can either go to the cinema or to the restaurant.

Sie isst weder Fisch noch Fleisch.
She eats neither fish nor meat.

(Also, if someone offers you two options and you want to reject both, you can just say weder noch to mean "neither one.")

Sowohl literally translates to "as well (as)" and is usually combined with als auch or wie to indicate that two things are both true. The sentence structure is a little different from English, though. We put "as well as" or "and" in between the two items, but sowohl goes before them. The nearest English equivalent in terms of sentence structure is "both/and":

Dieses Gerät spart sowohl Zeit als auch Geld.
This appliance saves both time and money.
OR This appliance saves time as well as money.

sowohl im Inland wie auch im Ausland
both at home and abroad
OR at home as well as abroad.

Je/desto expresses a relationship between two comparative adjectives:

Je mehr du redest, desto dümmer klingst du.
The more you talk, the dumber you sound.

Zwar usually translates to "indeed" or "granted" or "it's true." It's frequently used with aber ("but") to partially concede an argument or fact but still maintain an opposing position:

Er mochte sie zwar, wollte sie aber nicht heiraten.
While he certainly liked her, he did not want to marry her.