If my partner opens one heart, and I respond one spade, am I showing four or five spades?
In Standard American bidding (and 2/1 game forcing for that matter), after partner's 1H opening, 1S promises at least 4 spades. After 1H-1S, partner's mostly likely calls are 1NT (5332 shape with no more than 14 HCP), 2 of a minor (5-4 or better in the bid suits, may have anything short of a game force in terms of values), 2H (6+ hearts, probably less than 17 high card points), 2NT (18-19 HCP, 5332 shape), or some number of spades.
After 1H-1S-1NT, your rebids:
After 1H-1S-2H: - 2S: This shows a weak hand with 6 spades or better and likely a heart void; why else correct from partner's 6-card suit to yours?
Obviously, this doesn't cover all the bases, but it lays out some of the most common situations.
You need only four spades to respond one spade.
When your partner opens, you are expected to try to keep the bidding open if possible. That's why you need only four of a major to respond, and as little six points (although you may have a lot more). The fact that you have four spades is valuable information. Your bid (in a new suit) is forcing, meaning that you will get a chance to bid again and show your other values.
A small percentage of the time, partner will be 5-4 in hearts and spades, and be able to raise spades, and you'll have a 4-4 fit.
More often, there will be a try for a no trump contract. Partner may bid no trump if spades is the only suit where s/he is short. If partner is 5-4 in hearts and a minor, the minor will be bid, and if you have the other minor, you can bid no trump.
Occasionally, you'll find a 4-4 fit in a minor, and make a part score. Game is unlikely unless you and partner have at least 28-29 points between you.
One spade over one heart may indicate transfer to 1NT by opener as one spade may have weak hand with minimum 3 carder weak Spade. After 1NT rebid it is passed so that strong hand does not become dummy