After partner’s takeout double, responder has to decide two things: which suit to bid, and which level to choose. Bid your longest suit, preferring a major, even if you hold only four cards in the suit.
Points need to be carefully shown too:
0-8 points, bid your longest suit (preferring a major) at the lowest level e.g. ♠963 ♥Q4 ♦T82 ♣QJ864. The bidding goes 1♦ on your left, partner doubles, next hand passes. Bid 2♣ your longest suit, showing 0 - 8 points.
9-11 points, jump a level in your longest suit e.g. The bidding goes 1♥ on your left, partner doubles, next hand passes. Jump to 2♠ showing 9 - 11 points (and possibly only four spades).
12+points, go to game in your longest suit, or cue bid opener’s suit if you’re not sure of the best spot (this shows a hand with four cards in each major. e.g. ♠AQ642 ♥85 ♦K963 ♣K9. You hear 1♥ on your left, double from partner, pass to you. Jump to 4♠.
if you held ♠AQ64 ♥KJ85 ♦9 ♣K1098, and your left hand opponent bid 1♦, partner doubled, to you, now you should try 2♦, suggesting both majors, asking partner to pick the better contract.
No trumps is not ideal, (because your partner has shortage in opener’s suit), but sometimes responder has controls (stoppers) there. You hold: ♠86 ♥AJ10 ♦Q1054 ♣Q1072 Your left hand opponent bids 1♥, partner doubles, to you. bid 1NT. With two more points, bid 2NT.