This is kind of my favorite thing to do at the moment. My strategy is usually:
1. Trade everyone for prospects.
Like vega said ^ tank without shame. You want the top pick, and you want to sign him, no matter what. You want to dump everyone who isn't cheap or in early arbitration, and you want to demand prospects in return. If you have to take on some one-year crap contracts to get those prospects, do it. You're not going to win for two years, so don't hold on to anyone in their prime or you won't be able to afford.
And you want to finish deep dead bottom last. If there's another team out there who sucks, out-tank them. Use terrible relievers as starting pitchers if you need to (has the added benefit of not injuring your starters as often). Play guys out of position so they rack up errors, and they might get some secondary position points.
2. Watch your owners' goals
"Two out of three" is usually good. You should be able to meet any attendance goals just by dropping the ticket price. Your young guys are going to be cheap, so you can cut tickets in half and still balance the books. Sometimes you can't upgrade a position right away. Don't try, focus on the other things. This is going to be somewhat important since you're going to lose a ton of games and get a really low score that first year.
3. Invest in coaches. Find them, recruit them. Focus on pitching first, and try to match your young starters' tendencies with coaching strengths that will support them.
4. Keep your eye out for cheap additions - sort that free agent list early and see if you can find guys under age 25 with 2-star or better potential you can sign on a minor league contract. Also, the Rule 5 draft is a way to add a couple of gems you can be patient with, so clear a couple roster spots going in.
5. Good defense is usually more available than power hitting, and both can be valuable. When you're ready to turn it around, fill in your defense through free agency, and it doesn't hurt to pick up some depth. Even if your guys are fragile, if they fall out of the lineup it won't matter because all your guys are the same - great glove slap-hitters.
That's my two cents
