The UG is rather similar to the UK Limited, which is what German companies were using before due to onerous regulations. There is a standard protocol that you can modify to match your setup. You pick a company name, check with the local chamber of commerce to make sure it's not in use, and submit the documentation to a notary. You don't have to prove anything except that you are in possession of initial capital (may be any amount greater or equal to 1 euro) and have not been sentenced for fraud. The notary issues a document that you can use to sign up for a bank account. You go to the bank with it, and give them the initial capital, which they deposit into your company's new bank account. You only have to prove identity and place of residence of the company. It's easiest initially to register your company's place of residence as your own address. It's easy enough to change later. The bank gives you a proof of payment, which you give to the notary, and the notary signs off on it and forwards your case file to the trade registry. You pay the notary (you can make this payment from the new corporate account or from your personal funds). The trade registry sends you a bill, which you pay. Then you get entered into the registry and sent proof of this. With this registry entry, you have a company. This document is proof of your company's existence. The tax authority will send you a questionnaire asking you to estimate the income of your first two years. This is an estimate, and is nonbinding (but it's easier later if you guess approximately right). You fill that in, and you get issued a tax number. With that tax number, you can issue invoices, and file tax reports. In addition, you need to write yourself an employment contract if you receive salary. Now, the UG is a restricted variant of the most common company format in Germany, the GmbH. There are restrictions on the number of shareholders and the amount of profits that may be paid out to shareholders. You are required to hold a quarter of profits each year until you reach the minimum capital of a GmbH. You can then ask to be reentered into the trade registry as a GmbH, and the restrictions are lifted.
The tax authorities will happily tell you what you need to be aware of when you first sign up, and will remind you with sternly-worded letters if you miss anything. The company registration process takes a couple weeks of running around, at most. There is an issue you need to be aware of though - company registration information is public. This means a number of stationary, supplies, and whatnot peddlers will send you junk mail. Do not put an email address in your company registration data. A number of scammers will attempt to get you to pay frivolous bills. If you receive a bill for several hundred euros from a company you never heard of claiming to be a government agency, throw it away.
In summary, it's not easy, and it's not impossible. Nowhere is a business plan or proof of competence required, nor large amounts of capital. You will get asked a LOT of questions if you apply for a loan or insurance with a fresh company with 1EUR starting capital, but that comes with the territory. Getting a company credit card or bank account is no issue at all.