As mentioned by a number of posters, relationships are of utmost importance. However, deal structure does matter.
The old-school "country club" structure is:
Investor puts up 100% of the capital and Operator puts up 0%. Investor gets his/her initial capital returned, then a 6-8% preferred return, and then all profits are split 50/50 between Investor and Operator.
The negative here is you'll often get push-back because the returns to the Operator are disproportionate to the risk they're taking (zero cash investment). Also, most lenders don't want an operator to have no cash in the deal.
A more modern private-equity structure is:
Investor puts up 90% of the capital and Operator puts up 10%. The Investor + Operator both get their initial capital returned, then both receive a 6-8% preferred return, and then profits are split based on hurdle rates (this is commonly referred to as a waterfall). As higher hurdle rates (returns) are exceeded, the Operator receives a disproportionate share of the profits. Thus, the Operator is rewarded for better returns to the partnership. The Investor should always grant incentives to the Operator so he/she works hard for great returns.
The realty:
Smaller private deals (under $15MM) usually end up somewhere in between these two structures. Your goal as the operator is to negotiate the best deal for yourself while providing your investors with strong returns to keep them coming back for more. I've seen plenty of successful operators negotiate deals in which then end up with roughly 50% of the total returns; their investors were quite sophisticated, too.
Larger deals often require more-sophisticated investors. These investors will negotiate harder and drive down your share of the upside.
Ultimately, the best way to raise money for an acquisition is to tie up a great deal! They are so few and far between that you'll easily raise money. And if you still struggle, call up an experienced market participant and partner with them.