If you need to get the audit details of an entity record here is a simple code using the SDK API of CRM:
First, we need to get the audit collection of the entity record:

            QueryExpression auditQuery = new QueryExpression();
            auditQuery.EntityName = "audit";
            auditQuery.PageInfo.PageNumber = 1;
            auditQuery.PageInfo.PagingCookie = null;
            auditQuery.ColumnSet = new ColumnSet(true);

            FilterExpression filter = new FilterExpression();
            filter.FilterOperator = LogicalOperator.And;

            ConditionExpression condExp = new ConditionExpression();
            condExp.AttributeName = "objectid";
            condExp.Operator = ConditionOperator.Equal;
            condExp.Values.Add(recordId); // The record Id to get the auditing
            filter.AddCondition(condExp);

     // You can add here another condition to get the audit of a specific date using the created-on attribute filter

            OrderExpression order = new OrderExpression();
            order.AttributeName = "createdon";
            order.OrderType = Microsoft.Xrm.Sdk.Query.OrderType.Ascending;
            auditQuery.Orders.Add(order);
            auditQuery.Criteria = filter;

            EntityCollection auditCollection = Service.RetrieveMultiple(auditQuery);

Then we need to get for each audit retrieved, the details to see the difference of the attribute value:

foreach (Entity audit in auditCollection.Entities)
{
string action = audit.FormattedValues["action"].ToString(); // The action of the change for ex. Create/Update/Delete
RetrieveAuditDetailsRequest auditDetailsRequest = new RetrieveAuditDetailsRequest
{
        AuditId = audit.Id
};

RetrieveAuditDetailsResponse auditDetailsResponse = (RetrieveAuditDetailsResponse)Service.Execute(auditDetailsRequest);
if (((AttributeAuditDetail)auditDetailsResponse.AuditDetail).NewValue != null)
{
   if (((AttributeAuditDetail)auditDetailsResponse.AuditDetail).NewValue.Attributes.Count > 0)
      {
          var oldDetail = ((AttributeAuditDetail)auditDetailsResponse.AuditDetail).OldValue; // The Old value
          var newDetail = ((AttributeAuditDetail)auditDetailsResponse.AuditDetail).NewValue; // The New value
      }
}
}

Enjoy it!