Normally you shouldn't actually be manually setting either the start date or
the start time for tasks at all, except under very specific and relatively
rare circumstances. Instead, you should be allowing Project to calculate
them for you based on the Project start date, the functional relationships
between the tasks as expressed through dependency links, and the durations
of the tasks that leading up to the task in question. Once you assign the
resources to your tasks, you might find two tasks in conflict such as you
describe. Running the resource leveling tool (Tools menu) after assigning
the resources will delay one of the tasks until the time conflict is
resolved just like you say you want to do.
If there's some reason you can't do it as I've described and you simply must
enter the start date and time, all date fields in Project (such as the task
start field) are actually date/time fields and include the time even if you
don't see it. To set your second task to start at 9am instead of 8, when
you enter the start include the time as well as the date in your entry
"01/15/05 9:00 am." To see the times, in the Tools, Options menu, View tab,
select a date format that includes the time as well.
The "Work Is Entered In" setting of "hours" has no bearing on this. It
refers to whether resource work is entered and displayed in hours, days,
etc. Work is usually expressed as man-hours and expresses the energy the
resources are putting out. It is NOT the length of the task such as you see
displayed or enter in the duration column. Duration measures time, work
measures sweat and while they both can use hours and may happen to be the
same number some of the time, they are not measuring the same things and by
no means are they always the same number. Make very very sure you're not
mixing them up and using them interchangeably. (Your post sounds like
there's a real good chance you might be.)