Like any other attribute, you can specify classes with a JavaScript attribute, seen here:

<button
  class="{current === 'foo' ? 'selected' : ''}"
  on:click="{() => current = 'foo'}"
>foo</button>

This is such a common pattern in UI development that Svelte includes a special directive to simplify it:

<button
  class:selected="{current === 'foo'}"
  on:click="{() => current = 'foo'}"
>foo</button>

The selected class is added to the element whenever the value of the expression is truthy, and removed when it's falsy.