If your suit was diamonds or hearts, then you would bid your suit over 3♣ and partner would be expected to pass.

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If partner advances with 3♦ then you will be able to bid a natural and forcing 3♥. If partner happens to bid hearts over 3♣, you can raise to game. If partner bids 3NT then you can Pass.

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Start with a forcing 3♣. Plan on looking for a slam. 5♣, 6♣ and either game or slam in notrumps are allpossible contracts.
If partner bids 3NT over 3♣, you can make a quantitative raise to 4NT.
If partner bids a red suit, you can continue with a 3♠ cue-bid, asking for a spade stopper for notrumps. If he shows one by bidding 3NT, again you can raise to 4NT. If he does not, you can still investigate slam in clubs.
These sequences cover all ranges of unbalanced hands, from those that just wish to compete the partscore, through those seeking the best game contract, all the way up to hands wanting to investigate slam.

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If you wanted just to compete the partscore, you would have bid 2♠ at your first turn. If you wanted to force to game, you would have jumped to 3♠ immediately over 2♥. This sequence, shows an invitational hand, usually with a six-card spade suit. Partner either passes or raises to game.

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Cue-bidding the opponent’s suit promises four cards in the unbid major (or in at least one major if the opponent’s suit is a minor). Bidding directly denies a stopper in the opponent’s suit.

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Bidding 3NT denies four cards in the unbid major (or in either major if the opponent’s suit is a minor). Bidding directly denies a stopper in the opponent’s suit.

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Cue-bidding the opponent’s suit promises four cards in the unbid major (or in at least one major in the opponent’s suit is a minor). Starting with the Lebensohl 2NT shows a stopper in the opponent’s suit. “Slow Shows” is the way to remember.

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Bidding 3NT denies four cards in the unbid major (or in either major in the opponent’s suit is a minor). Starting with the Lebensohl 2NT and then bidding 3NT shows a stopper in the opponent’s suit (“Slow Shows”).

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You can now bid 3♠. Partner knows you do not have a five-card suit (you would have jumped to Three Spades at your first turn), so the implication is that you have spades and are worried about hearts. Suppose partner’s hand is something like: ♠K7 ♥J73 ♦AJ3 ♣AQT63
You can easily avoid playing in a silly 3NT and, instead, find your way to 5♣:

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You can still bid 2♦, natural and non-invitational.
You can also show a hand that wants to compete in clubs (2NT intending to pass partner’s forced 3♣), or a game-forcing hand with one minor via a natural three-level bid in either suit.
Starting with 2NT and then bidding 3♦ over opener’s 3♣ is invitational.

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What do various bids in the majors mean? There is no standard method. A workable method, is to use 2♥/2♠ to show a hand with both minors. 2♥ shows better clubs, 2♠ shows better diamonds. Partner should just pick his best minor.
If you have game-going (or stronger) values, you will bid again after partner has given preference. You might advance by bidding a major where you hold a stop, to give partner a choice of bidding 3NT: In this auction your hand is known to be balanced (ie no singletons), which may help partner to choose between 3NT and a minor-suit game.

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With both minors, game-forcing values and a major-suit shortage, you start with a splinter-bid on your first turn. It may show a hand such as: ♠K73 ♥5 ♦AQ84 ♣K9643.

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This usually shows a hand with no direction but with enough values to know the hand belongs to our side. For example: ♠KJ83 ♥J5 ♦AJ4 ♣Q943.