It really depends on the situation. Do you need the help? Are you really prepared to split the profits?
Start writing down all of the tasks that need to be done to start up and operate your business (ie Legal, Financial, Design, Merchandising, Supply Chain, Production, Marketing, Sales, Distribution). The figure out which areas you are good at and want to focus on. Then figure out which areas you can outsource to professionals. If there are no areas left, then you can start by yourself. If there is a gaping hole that needs to be filled, then maybe finding a partner is a good way to go.
The biggest value of a partnership is when each partner brings a different skill set to the table that ultimately compliments each other to make the business successful. Just make sure you document what each partner invests and what each partners responsibilities are. And then based on that, figure out what each partners ownership percentage should be. And each partner should understand that ownership includes being liable for expenses and losses, not just revenue and profit.
Are you a talented, professional designer who can create artwork that specifically fits the target audience of your brand? If so, then do it yourself. If not, then hire a designer.
Do a Google search for "starting a business in (your state)." You will find plenty of resources with great info on what you need to get started.
But generally, you need to register your business, apply for tax id number and apply for a sellers permit.
Overseas production is usually cheaper than domestic production. But, minimums are very high and there are shipping and import costs as well. Unless you are ordering thousands of units, you are better off using US suppliers and local printshops.
If you did want to outsource overseas, China and India seem to be the most common. If you wanted to look into South America production, Honduras is pretty common.
Depends on your target market. Are you developing a brand targeted towards consumers who will value - and pay extra for - an eco friendly product?