• Suit CSS, BEM et al.: separate, regular stylesheets but component naming convention for components.
• Just manually with inline style attributes. To merge multiple style maps, use helpers like react-style, which enables an array syntax for the style attribute, use a custom function like m() to do the same, or use destructuring: style={ {...a, ....b, ...c} }.
• Radium supports a [] syntax like react-style, but also adds support for things like :hover and media queries at the expense of wrapping the component.
• CSS Modules is a CSS-like syntax that gets parsed into a dict of class names, and the CSS extracted into a file.

Further reading:

• A very complete article discussion the different options
• A crazy list of projects trying to tackle the issue