I don't know the whole structure of your table, but this might give you something to start.
You might need to add some fields or add the extra time to get the 00:59:50.
Be aware that BETWEEN is inclusive for both values, so you might have values that get in two days.
CREATE TABLE #PSACCESSLOG(
opridvarchar(6),
logindttmdatetime)
INSERT INTO #PSACCESSLOG
SELECT 'jbaker', '2012-06-01 00:50:59.000' UNION ALL
SELECT 'jbaker', '2012-06-01 12:50:59.000' UNION ALL
SELECT 'jbaker', '2012-06-01 15:50:59.000'
SELECT oprid,
DATEADD( dd, DATEDIFF( dd, 0, LOGINDTTM), 0) AS LOGINDT,
COUNT(*) AS entries
FROM #PSACCESSLOG
WHERE LOGINDTTM BETWEEN '2012-06-01 00:50:59.000' AND '2012-07-01 00:50:59.000'
GROUP BY oprid, DATEADD( dd, DATEDIFF( dd, 0, LOGINDTTM), 0)
ORDER BY OPRID, LOGINDT
DROP TABLE #PSACCESSLOG