The first step to playing Splinterlands is to start with campaign mode.
Campaign mode is free and teaches you how to play, and it also gives you cards.
The second step is frontier mode: a free game mode.

I've written some posts about campaign mode and Frontier Mode that might be useful for you to get started ;)

https://ecency.com/post/@libertycrypto27/my-experience-in-the-new-compaign-mode-32-foundation-cards-and-1100-glint-earned-engita-bzy
https://ecency.com/post/@libertycrypto27/splinterlands-new-prologue-and-new-chapters-of-campaign-mode-completed-10-starter-packs-bought-and-opened-engita-98p
https://ecency.com/post/@libertycrypto27/splinterlands-the-new-free-to-play-frontier-format-is-live--my-first-frontier-battles-and-my-first-reward-engita