Signing up is free and self-serve: go to dashboard.cohere.com, create an account with Google, GitHub, or an email and password, and Cohere's pricing FAQ says a trial API key (a password that identifies your app, and that spends your money) is created for you automatically and shown in the dashboard's "API Keys" section. You need to have reached the age of majority where you live to accept the terms.
You will almost certainly not need to pay while you are learning. Cohere's pricing table currently lists Command A+ as free for both "API key" and "Model download," and Cohere's model documentation says that "for both trial keys and production keys, Command A+ is free until rate limits are reached." The models that do cost money are the smaller and narrower ones — such as Command R, billed per million tokens (a chunk of text, roughly a short word — how AI usage gets counted) of input — and you have to choose them on purpose.
Free here has a contract attached, not just a ceiling. Cohere's pricing page states that trial keys "are rate limited and are not permitted to be used for production or commercial purposes," and its rate-limit docs currently put chat on a trial key under both a per-minute and a monthly call cap. So the free key covers learning and prototypes; the moment something you build takes money, it needs a production key, which bills pay-as-you-go and is requested from the Billing and Usage page by an account owner.
Cohere is built for people putting AI inside software, and most of it is reached from code. The part you can reach in a browser is the Playground, which Cohere's docs describe as a message box with a model picker — you may need to check what it actually offers once you are signed in. If you have never used an AI tool at all, an hour with a chatbot from Text & Conversational AI first will make everything here land better, and Cohere will still be waiting.