The anthem itself:

Unbreakable union of free states
Great Russia¹ (has been) united forever²
Yes, (it) lives the constituted will of the people
United³, powerful Soviet⁴ Union.

[Refrain:]
Praised be our father's land⁵, our freedom
Friendship of the people⁶ is a safe fortress
Party of Lenin, power of the people
Leads us to the triumph of communism.

Through the thunderstorm we see the shine of the sun
And Lenin the Great brightened our way⁷
He lifted/brought the people to (higher spheres of) the right matters
Inspired us for work and exploits⁸.

[Refrain:]
See here ...

In the triumph of the never-dying idea of communism
we see the future of our country
And under the red banner of our glorious fatherland
We will forever and always be⁹ (on the) right (side).

[Refrain:]
See here ...

Explanation of terms (i.e. footnotes):

1. Rus was a tribe of nordic warriors that "invaded" Nizhni Novgorod, which then became the very first Russian city. It was inhabited by Eastern Slavs (there are many tribes, but the Slavonic languages are divided into three groups. Western [e.g. Polish], Eastern [e.g. Russian] and Southern [e.g. Bulgarian] Slavonic). Actually nobody is sure wether they invaded the city or wether they had been invited.
2. The meaning of the word comes from "for centuries".
3. Can also mean "only" (i.e. unique).
4. Soviet means "advice" or even "council".
5. I.e. "country".
6. I.e. "nations".
7. I.e. "journey".
8. Heroic actions ...
9. Probably in the context of "to fight".