How do I protect my designs and t shirt slogans for others copying and selling my ideas?
This is not legal advice, just opinion. If you want/need legal advice, you should talk to a lawyer.
You can't protect someone from stealing your idea. Unfortunately, it doesn't work that way.
There's no "shield" or "block" you can buy or register that would stop someone from the physical act of taking your designs or ideas.
However, you can register your completed designs as a copyright with the US Copyright office (assuming you are in the US). This won't "stop" someone from actually taking it, but it will show that you created the design first and give you more legal standing if you decide to legally try to stop someone from using the design.
T-Shirt "slogans" generally aren't copyrightable, however, if you can prove your t-shirt slogan is also a "brand" (like "Just Do It" or "Life is Good"), you could qualify for a TRADEMARK. This still wouldn't "stop" somoene from actually taking it (unless they were conscientious enough to search the US trademark database and decide not to move forward on their own if they saw it was registered). However, owning the trademark can help you have more legal standing if you want to get people to stop using your brand name without your permission.
Many t-shirt lines have been started and run successfully without filing a single trademark or copyright. Many t-shirt lines have been started and run successfully by filing for a trademark for their brand and a copyright on each design.
You need to have money to file a copyright and money to apply for a trademark (use the links in the "Resources" section off to the left hand side menu of this site). You would also need money to hire a lawyer to protect your copyright or trademark.
My personal opinion is that people are "generally" overly worried about people stealing ideas/designs. Does it happen? Yes. But I think more often than not, if you have an original design, your best bet is to get that design onto some t-shirts and start selling before someone else does. If it's your original design, you probably have more passion, ideas, and marketing methods since you originated it. You can probably sell your design better than anyone else could. By selling it first, you can establish yourself as the "original" and you can even get a reality check to see if your idea/design is as great as you think it is.
That's just my opinion though.