Purchasing an existing business involves a different skill set and collection of chores. First of all, you would be unlikely to become trapped in the producer role, since your purpose from the beginning would be to manage the business. Therefore your view of the business will be markedly different.
I provide this preamble description of the 2 differing methods of business entry because they are important in finding a business to buy into. You find a particular business the same way you would approach the finding of a customer–by targeting and prospecting.
Start in areas in which you have expertise. You should also contact business associations in the specific field you have chosen and ask if they know of any target businesses. After adding in geographical, financial and other preferences or criteria, you should then be able to winnow this large sector down to a few target businesses.
The next task is to approach these businesses and enquire if they are considering taking in a partner or have succession issues. Be diplomatic, but honest. You do not want to look like a vulture hoping to scoop up a broken company for a cheap price. Rather, your position should be that you want to operate a business in this field and are looking for an opportunity that would provide some challenge, interest, financial return and personal "fit" (or comfort).
Be clear about your desires and goals, because they will be important in any partnership into which you might enter. Your approach will speak volumes to potential partners about your style. In essence, you are selling yourself to potential partners, and the secret of any sales campaign is to make the prospect want you, not the other way around.
As to what vendors will be looking for in terms of succession, visit the succession planning advice section on the BDC site to get a flavour of the most common issues. You might also want to consult family business associations and some books on these issues.
Generally, however, owners of businesses take in partners or sell their business because they want to retire or slow down; because they have no one in the family who can take over the reins; because they need an interim manager while their family successors learn the business; or because they are just tired of the business itself.
One word of warning: Some business owners want to sell because their businesses are failing and they have no desire to fix them, or because they need quick cash but want to retain absolute control. Businesses like these will be disastrous for any new partner or operator. Avoid them.