Invented by world champion Oswald Jacoby, the Jacoby Transfer is a popular convention that can improve your notrump bidding. To use this convention, you and your partner agree to change the meanings of your diamonds and hearts responses after you open NT. Jacoby transfer is used by the responder whose partner has opened the bidding with 1NT, 2NT or 3NT. As the name of the convention indicates, the responder will transfer the No Trump bidder to a more favorable suit.

Responder uses one of these artificial bids to describe any hand (of any strength) that has a 5-card or longer major suit with 0+ points.

After partner opens 1NT a bid of:
2♦ - shows 5 hearts
2♥ - shows 5 spades.

The Jacoby transfer saves bidding space and gives responder an easier, more accurate way to show his strength later in the auction. It also makes the 1NT opener declarer, which can be an advantage. A disadvantage is that gives up the ability to sign off in 2D if you have real diamonds.  

The 1NT opener must accept the transfer by bidding the next higher suit.  A lot of new players bid 2NT when they don’t have three of partner’s suit. This should never be done.  Partner could have 6 or more when she transfers.  Partner may also have no points and need to play 2 of the major where she can take some tricks with her suit as trumps instead of 1NT where her hand is useless.  You also take away the follow-up bids by bidding higher than the next suit.

If partner opens 1NT, use the Jacoby Transfer with any hand that has a 5+-card major suit. After partner bids your suit, choose a rebid that describes your hand further. Here are the meanings of your second bids after the auction:

1NT by partner -- 2D (transfer) by you
2H by partner   -- ?

• Pass = Weak hand (0-7 pts.).
• 2NT = Invitational to 4H or 3NT, exactly 5 cards in your suit. (8-9 distributional hand)
• 3NT = Game values for 4H or 3NT, exactly 5 cards in your suit. (10-15 distributional hand)
• 3H = Invitational to 4H, 6 or more cards in your suit. (8-9 distributional hand)
• 4H = Game values, 6 or more cards in your suit. (10-15 distributional hand)
• New suit = Forcing to game, showing a second suit.

If responder transfers and then rebids notrump or a new suit, opener must decide whether to play in notrump or in partner's suit. Always choose partner's major if you have 3+-card support. If partner's rebid was invitational, you must also show your strength by choosing the right level. If responder transfers and rebids 2NT (invitational), you should:
• Pass with a minimum opening (15 pts.) and 2-card support for partner's suit.
• Bid 3♥ with 15 pts. and 3-card support.
• Bid 3NT with 16-17 pts. and 2-card support.
• Bid 4♥ with 16-17 pts. and 3-card support.

I would play Jacoby Transfers and Stayman on over interference of a double (X) or 2C bids.
So, 1NT-(X)-2♦ is still a transfer to hearts. 1NT-(2♣)-2♥ is still a transfer to spades. While 1NT-(2♦)-2♥ is not a transfer.
When the opponent’s overcall is 2♦ or higher, it takes away both Stayman and the transfer bids, so our agreement is that  transfers are off after a 2♦ or higher overcall.  

2C - (P) - 2D - (P)
2NT - (P) - 3D*/3H**

*     3D  -  this is a Jacoby transfer showing a 5-card hearts suit 0+points
**   3H  -  this is a Jacoby transfer showing a 5-card spades suit 0+points