How can I sell a product with someone else's IP?

If the person doesn't have a patent, trademark, or copyright on the thing you want to copy, then you can copy as much as you want. Current IP law in the USA is "first to file" (see: https://en.wikipedia.org/wiki/First_to_file_and_first_to_invent)

If the person has any of those things, and you want to copy them legally then you have to ask them for a licence.

If the person has any of those things, but doesn't have the money to sue you for infringement, then you might be able to copy it with legal repercussion. That wouldn't be very cool though.

There are many things in your questions.

1. If you want to sell a similar product, it means you have identified a market/niche that is not addressed by the current product. A good thing to do would be to contact the company and check for the option to get an Agreement where you could build a similar product - based on theirs - with some tweeks, making sure it is a win-win deal for both parties (you are not competing their product and they access a new market through you). Then you would not have to reinvent the wheel, you would leverage existing IP and knowledge they currently have for this product and able to go quick on the market.

2. If first option doesn't work or you want to compete them directly, then you need to build your own product, i.e. re-invent the wheel (more costs, takes time, etc.). In this case, you need to make sure you are not infringing their IP or any other IP that other vendor might have with similar products (as correctly indicated in previous Lee's comment).

You should not view IP from a strict "law" perspective, you should view IP as an opportunity to leverage other's people work in order to quickly and efficiently build solutions that's going to solve your customer's problem.

First, you need to identify IP associated with the product, if any. The best way to proceed would be to contact them and they will provide you with the relevant IP (patent or design registered with USPTO) and agreement terms for licensing the same.

You would need a license with that IP owner. If you're interested in using another Co's brand, trademark or IP, you have to have a License Agreement with that Co that authorizes your right to use their marks, within a product category, within a specific territory, to specific retail channels.

Having a best selling book on Amazon and a few other ebooks and copyright digital material, it's always nice to be contacted from thoughtful experienced entrepreneurs.
You should reach out to the IP owner privately and ask if they do revenue splits, licensing or have a joint venture program in place and how they work with partner/marketers.
Show them how you both can come out ahead with your proposal. Hope that helps.