best opening for black

what are best openings for black against 1. d4?

and against 1.e4?

d5 or Nf6 can be played

The Indian Game (1. d4 Nf6) is currently the most popular black opening against 1. d4, while the Sicilian Defense (1. e4 c5) is the currently most popular black opening against 1. e4. If 1. d4 is responded to with 1. ... d5, it means it's a closed game.

For 1 d4, I think that it is fairly common for a player to be advised to first learn the Queen's Gambit Declined. If nothing else, it is probably going to be easier to find recent introductory opening books like First Steps: The Queen's Gambit

https://www.newinchess.com/media/wysiwyg/product_pdf/7652.pdf

and The Queen's Gambit Declined: Move by Move.

https://www.newinchess.com/media/wysiwyg/product_pdf/7743.pdf

It might be a good idea to consider Discovering Chess Openings by GM John Emms (2006).

https://web.archive.org/web/20140627114655/http://www.chesscafe.com/text/hansen91.pdf

For 1 e4, I think the most common advice is for a player to first learn about 1...e5. Again, there is a fairly recent introductory book, First Steps 1 e4 e5 by GM John Emms.

https://www.newinchess.com/media/wysiwyg/product_pdf/7790.pdf

Again, it might be a good idea to consider Discovering Chess Openings.

He asked what's best, not what's popular.

Eating French Fries is more popular than eating Brussell Sprouts.  Does that make French Fries the best for you?

The answer is that there is no best.  The best against 1.d4 is whatever works best for you amongst "normal" openings (i.e. QGD, QGA, Slav, Semi-Slav, KID, NID/QID, Benoni, Dutch).

Against 1.e4, you have the "big 4".  The rest, while not totally unsound, are far shakier, but out of 1...e5, 1...e6, 1...c5, and 1...c6, it's what works best for you.  I play 1...e6 about 90% of the time and 1...e5 the other 10%.  Someone else may do better with 1...c5 or 1...c6.  Any other first move gives White a greater advantage.

TINSTAABO

"There is no such thing as a 'best opening.' Each player should choose an opening that attracts him. Some players are looking for a gambit as White, others for Black gambits. Many players that are starting out (or have bad memories) want to avoid mainstream systems, others want dynamic openings, and others want calm positional pathways. It’s all about personal taste and personal need.

For example, if you feel you’re poor at tactics you can choose a quiet positional opening (trying to hide from your weakness and just play chess), or seek more dynamic openings that engender lots of tactics and sacrifices (this might lead to more losses but, over time, will improve your tactical skills and make you stronger)." - IM Jeremy Silman (January 28, 2016)

https://www.chess.com/article/view/opening-questions-and-a-dream-mate

The April 2018 issue of Chess lists the top twenty openings compiled from a list of 2706 February games where both players were rated over 2400 Elo. One can not take position on this list too seriously because it is greatly influenced by how the openings are grouped. For example, all the Retis are grouped together, while English is separated into 1...c5, 1...e5, etc. Nevertheless, for what it is worth, some of the list entries are: 214 Retis, 127 Caro-Kanns, 123 King's Indians, 84 declined Queen's Gambits, 74 Slavs, 71 Nimzo-Indians, 66 Najdorf Sicilians, 56 Taimanov Sicilians, 53 Queen's Indians, 52 1...Nf6 Englishes, 51 1...e6 Englishes, 51 1...c5 Englishes, 51 Classical Gruenfelds, 49 Giuoco Pianos, 47 Kan Sicilians, and 45 Tarrasch Frenches.

"... A typical way of choosing an opening repertoire is to copy the openings used by a player one admires. ... However, what is good at world-championship level is not always the best choice at lower levels of play, and it is often a good idea to choose a 'model' who is nearer your own playing strength. ..." - FM Steve Giddins (2008)