A ‣ What are binomials? 
Binomials are expressions (often idiomatic) where two words are joined by a conjunction (usually 'and'). The order of the words is normally fixed. For example:
odds and ends: small, unimportant things, e.g. Let's get the main things packed - we can do the odds and ends later. (NOT ends and odds)
give and take: a spirit of compromise, e.g. Every relationship needs a bit of give and take to be successful.
You can often tell something is a binomial because of the sound pattern, which may be a repetition of the same first sound or a rhyme.
Tears are part and parcel of growing up. [an important part of / belong to]
The boss was ranting and raving /ˈreɪvɪŋ/ at us. [shouting / very angry]
The old cottage has gone to rack and ruin. [is ruined / has decayed]
He's so prim and proper at work. [rather formal and fussy]
The hotel was a bit rough and ready. [poor standard or quality]
She has to wine and dine important clients. [entertain / take out to restaurants]
They stole my wallet. I was left high and dry, with no money. [in a very difficult situation]
B ‣ Pairs of near synonyms 
At other times, the clue is that the words are near synonyms.
You can pick and choose - it's up to you. [have a wide choice]
My English is progressing in/by leaps and bounds. [big jumps]
It's nice to have some peace and quiet now that the children have left. [a peaceful/calm situation]
The doctor recommended some rest and recreation / R and R. [relaxation]
First and foremost, you must work hard. [first and most importantly]
C ‣ Binomials composed of grammar words 
Many grammar words combine to form binomials.
There are cafes here and there along the sea front. [scattered round / in different places]
We've had meetings on and off / off and on. [occasionally]
I've been running back and forth / to and fro all day. [to and from somewhere]
She's better now, and out and about again. [going out]
She ran up and down the street. [in both directions]
Language help
Your language probably has many binomials. Check that the ones which look similar in English have the same word order as your language. These three are very neutral binomials and can be used in formal or informal situations. Try translating them.
an old black and white photograph
Ladies and gentlemen, your attention, please!
She ran back and forth.
D ‣ Binomials linked by words other than and
You've got your sweater on back to front. [the wrong way]
He won't help her - she'll have to sink or swim. [survive or fail]
Slowly but surely, I realised the boat was sinking. [gradually]
Sooner or later, you'll learn your lesson. [sometime in the future]
She didn't want to be just friends - it had to be all or nothing.
Well, I'm sorry, that's all I can offer you - take it or leave it.
It's about the same distance as from here to Dublin, give or take a few miles. [perhaps a mile or two more, or a mile or two less]