Teespring

Hi,
In my opinion, the best methods are the ones that you are comfortable and can do consistently. With that being said - one method I like is Instagram, and I have seen good results in my page and also seen some other people get good results.
Start a page, brand it (logo, high quality photos, good color scheme, etc.)
start bringing followers - follow other people that like similar posts on in your niche and they'll start following you, build more and more good content, gain likes/comments (for instance - like content of other people that like this niche and many of them will like your posts as well), and keep going from there, promoting your products. If you'll get enough targeted people, you can start see sales and success.Once you earn money and have budget, you can also invest in shoutouts as well - where other people, instagram influencers, are promoting your stuff, many times for very low cost.

Of course, this is just one possible method and if you want to try it you'll need to learn it and dig a bit deeper.
I am sure other people here have more ideas:-)

Teespring pretty much covered much of these with good pointers on how to promote your campaign. You can either utilize Teespring tools as they do have free tools as well or through social media. Though Teespring marketing isn't really free, the fee is deducted from your profit. You can find more of these in their training center (specifically Chapter 3).

They also cover how to advertise on different social media platforms and provide good pointers on how to promote on it without the need of spending money on ads. (It's all in Chapter 4 of the Traning center)

You should check it out: https://community.teespring.com/training-center/

Facebook,Pinterest,& send to your email list as you build it

Try facebook traffic you can found a lot of courses on how to promote on facebook