Dear rickyj:
As foreigner, you may start any kind of business in uruguay (except very few excemptions). Nonetheless, in order to open and register a company, you have to personally sign some documents in presence of a local notary that will certificate your signature.
The other possibility is to use a power of attorney, so other person may sign in your name.
You may open a personal company, a limited liability company (SRL or LTDA, which need a minimum of 2 persons, that might be individuals or legal persons, or also you may open a public limited company or SA.
You can also register a subsidiary of foreign company.
Any type of company have different times of registering, different costs and different individual responsabilities, and depending of the kind of business you will start, one type would be more appropiated than the others.
In any case, remotely it is impossible to open and register a company, except by using a power of attorney, which should be legalized and translated into spanish if necessary, by a local official translator.
Do you have planned any particular business??
Regards.
Daniel Mascort