It is not easy to start designing T-Shirts. In fact, it is very difficult and very tedious. From researching a design idea, to picking a company to handle your printing and order fulfillment... it is a bitch.
Researching T-Shirt design ideas and the market, not just your competition, is more valuable than gold to a professional tee designer. It saves a lot of time and grief later down the road if you do your homework to avoid copyright issues and adding to an over saturated market place.
One piece of advice that will help you out on your t-shirt designing journey is to make a full commitment. This stuff is not easy. It is grueling work. There is Researching, Designing, Marketing, Networking, Customer Service, and more that must be done or delegated to someone else.
You will not become a success overnight. You will not make a fortune off your design or designs right away. You will not get instant traffic to your shop unless you have a ton of money to invest into it. If you have a shop at a Print On Demand service purchasing PPC ads is not worth the investment at all (It was around $5 a click last time I checked for T-shirt related keywords). If you are using a POD service, not all are created equal. If you are starting a clothing brand it will require more than your mom and brother sporting your label. And on that note, just because family or friends say the design or brand is good, doesn't mean everyone else will. Family is supposed to be supportive, the t-shirt wearing public however are a different animal all together.
I cannot preach having your own design or brand niche enough. As you can tell on the TeeFetch homepage there are a ton of pop culture mashups out there with just as many designers as their are concepts. I'd highly advise avoiding that niche unless you are on the same level as Zerobriant or Winterartwork. With so many DMCA notices flying around I would just avoid pop culture all together. Be original.
How To Start Designing T-Shirts.
Now for the basics of T-shirt designing. Get a program such as GIMP (it's free) or Adobe Photoshop CC and or Adobe Illustrator. Create your design on a HIGH RESOLUTION of 300 DPI TRANSPARENT BACKGROUND sized according to the Printing Service's guidelines that you are going for. Put your single colored line work on its own layer. Then a new layer for each color that you fill in. All the Red on a single Red layer, all the Blue on a Single Blue Layer and so on. DO NOT MERGE THE LAYERS. Try not to exceed 6 colors total if you are having your designs screen printed. For Direct To Garment printing it doesn't matter how many colors. PNG 24 format works great. Some sites like AI or EPS formats. It doesn't hurt to save your file as each type. Avoid JPG and GIF. And make sure you are designing with a Black tee in mind.