If this component is being used in the Lightning Experience, you want the component to implement force:hasRecordId
, which will give you the the object's id which you can use to query the other related information that you need. The only other field that can be populated in that manner is the name field, which you can get by having your component implement force:hasSObjectName
.
<aura:component implements="flexipage:availableForRecordHome,force:hasRecordId,force:hasSObjectName">
<aura:attribute name="recordId" type="String" />
<aura:attribute name="sObjectName" type="String" />
The Lightning Components Developers' Guide has a section on this topic.