The classic answer is develop normally--sometimes harassing the queen while doing so.
Overusing the Queen

I have found that very few are actually really good at using their queen alone, but they are in truth very annoying to play against. That is their personal strategy. I do not personally subscribe to that way of playing because I believe that playing chess is relatable to erecting a building or some type of structure. Meaning you cannot build a house with just one 2x4 and nothing else. Same thing with chess as it takes every chess piece to effectively win the war. You need as many of your pawns, your knights, bishops, rooks, queen and sometimes even perhaps the king to trap one piece, ie; most times the queen. Especially if she is brought out too early in the opening. Example: 1.e4 e5 2.Qh5. I agree with goldendog though that minor pieces should be developed normally to their classical squares in the opening as the game is about both sides preparing their defensive positions in order to get the king to safety and then going on the attack of the enemy king. No matter what time control is being played. Good column.

It will never really work at top levels, but it can work sub 1800 because the queen could be dangerous and it gets players out of the book fast. I've even thought about employing 1.e4 2.Qh5 as a relatively serious opening against anything below around 1600. We have a master here in town, (now 2000 level, in his 70s) who played at 2200 for probably 20 years, using only 1. e4 2. Qh5. Outside of just really, really terrible moves, if you study about any strange opening enough, for years, you'll know it better than your opponents and probably get a fine position with it, despite it being "technically' unsound simply because they won't have been able to study all of the tricky lines.
I call this sort of stuff "tricky" shit and it's actually one of the reasons it's sometimes harder to play somewhat weaker players in the opening. Just because a principle is violated, doesn't mean you'll know exactly how to exploit it unless you're a computer or really high level.
I am noticing that many beginners like to overuse their queen early in the game in lieu of developing their minor pieces. A typical situation is one where they have activated few pieces, and their queen can be found buzzing all over the board, trying to be as annoying as possible. I don't think this is a winning strategy, since it's really hard to checkmate with only a queen, but I'm not sure how to take advantage of this. Any help?