If your site does not rely on Flash, Silverlight, or other plugins you probably have a working mobile site however there are additional design and implementation concerns you should probably consider.
Most mobile devices do not provide a mouse pointer so sites which depend on mouse-over or hover interactions can be unusable.
Does your site work well on high latency, low bandwidth network connections? Are you serving large images to mobile devices? Can your web servers handle a large number of long-lived slow requests?
Does your site server reasonable markup to enable user interactions? For example HTML5 input elements with input types will allow mobile devices to present an appropriate keyboard (email, numeric) or other interface (date pickers and so on).
Finally does your site's design work on small screens and viewports? The phrase you're probably looking for here is "responsive design". Both Bootstrap and Foundation provide support for flexible grids which can scale as percentages of the available viewport or be adjusted using media queries to jump between several specific layouts depending on the rendering device's viewport size.