As far as I know, this isn't something that is going to be very easy to do within Salesforce. Are you looking to get all of their actions, such as when the login, create records, edit records, etc or are you just looking to get a history of their chatter?
To get a list of all of their actions, you are going to need several SOQL calls to call each object type with a where clause like:
WHERE (CreatedDate = TODAY AND CreatedBy = :userId) OR (LastModifiedDate = TODAY AND LastModifiedBy = :userId)
You will need to run a SELECT statement on every object that you are looking to get this for. It isn't going to be a simple process unfortunately.