You can perform validation one of several ways (all of which are basically the same).
First, you can choose to run normal JavaScript using the onblur attribute, like this:
<apex:inputField value="{!MySetting__c.Value__c}" onblur="validate(this)" />
Second, you can choose to run managed JavaScript using the onblur function, like this:
<!-- Requires round-trip to server! -->
<apex:inputField id="value" value="{!MySetting__c.Value__c}">
<apex:actionSupport event="onblur" action="{!validate}" reRender="value" />
</apex:inputField>
Note that this method requires a round-trip to the server if you specify an action attribute, which may cause the form to lose focus.
Third, you can choose to bind to the onblur as you would in any normal JavaScript (given in jQuery for simplicity):
$("input[id$=value]").on("blur", function() { ... });