How this gets arranged depends a lot on where the money is coming from.
If you are interested in working with a university on government-funded projects (or other third parties that act similar to government funders, e.g., research foundations), then it's pretty straight-forward. For many such funding programs, companies are just as eligible as universities to bid as either a prime contractor or a subcontractor. You thus form your research collaboration just as though you were both universities (or both companies, if you're more familiar with that) and bid jointly. With a business involved, some programs will not be applicable (e.g., you are not "Young Faculty") but many others are specifically targeted to small businesses---SBIRs and STTRs, for example, are set-asides specifically designed to enable small-business R&D and partnerships with universities. You'll need to figure out how to comply with government contracting rules and your contracts people and the university's contracts people will need to come to terms (every university has its own unique procedures), but this is a very normal and well-supported interaction.
If you want to fund the laboratory's research from your company's own funds, on the other hand, it may become a bit more difficult. Universities are often well set up to handle this as well, but it more usually comes from large businesses rather than small businesses, and you are likely to find the arrangements much stickier, particularly regarding IP and publication control. This is because you are a small business, and so the risks involved in taking your money are much more difficult for the university to predict and manage than the risks involved in taking money from a large company. Still, if there is motivation on both sides, it's likely to be doable, and again, every university will have its own procedures.
In both cases, the right starting point is probably not money, but engaging the PI(s) you want to work with on an intellectual and scientific level. The really good sort of people that you would probably like to work will will have many possible options available to them, and you're much more likely to get good results in this fashion rather than taking the chance that they may feel you're trying to "buy their science." Once you've got intellectual buy-in, your primary PI contact will know the starting point in the university's contracting organization, who will in turn be able to hand off to others as needed to work out the contractual particulars of the deal.