It largely depends on the position that you're applying for.
In the past, you could get by with just a high school diploma. But today, companies are putting a lot of focus on the customer experience, so the requirements have shifted.
Keep this in mind when applying for a job. It's likely going to be a lot harder to get a job providing technical support for an e-commerce provider than for a clothing company or bank.
In many cases, you'll need strong customer service experience and a demonstrated ability to use customer relationship management (CRM) tools. The company will want to see that you can provide excellent customer service and move quickly when interacting with customers.
It also helps to have prior and relevant work experience and strong language skills. Bilingual customer service representatives are always in demand.