New 4 prong dryer but have a 3 prong outlet
Your dryer wants the modern, safe NEMA 14-30 recep.
Your house has the obsolete, dangerous NEMA 10-30. If the neutral wire has a common problem, it will electrify the chassis of the dryer.
So you can, but you shouldn't.   Here are your options:
LUCKY: There's a 4-wire cable underneath that 3-prong outlet ($15)
Turn the breaker off. Unscrew the receptacle and go see.
If you see either a ground wire, or metal conduit going back to the service panel, you're in luck.  You can simply change the receptacle to NEMA 14-30 and you are done.  Metal conduit is a valid grounding path.
This happens a lot, because Goober gets a used 3-prong dryer, doesn't realize you can easily change the cord, and so Goober changed the receptacle from 4-prong to 3.  Home Depot still sells the receptacles, which they should not.
SUPERB: Fit a 30A, 2-pole GFCI breaker ($95)
At your service panel, find the 30A breaker powering that outlet.  Change it for a 2-pole GFCI breaker.  (this requires that GFCI breakers be available for your panel: Eaton, Cutler Hammer, Bryant, Challenger, Square D, Murray, Siemens and GE are available many places. A few others are supported by Eaton CL breakers. For Pushmatic, Zinsco and FPE you're out of luck, but in the last two, your panel is actually dangerous and should go ASAP.)
After upgrading the breaker, change the receptacle to NEMA 14-30 and don't hook up the ground wire.
Finally, stick two stickers next to the receptacle:

GFCI Protected - reset at panel
No Equipment Ground

And you're done.  This is safe as houses. It would be almost impossible to kill yourself with your dryer even if you were intentionally trying.
GOOD: Retrofit a ground wire. ($20++++ depending on luck of route)
Run a 10 AWG separate ground wire, bare or green, from the dryer receptacle area (leave 1' extra slack) back to any of the following places:

The service panel where the breaker is
any junction box with a metal conduit path back to the panel
any junction box that has a #10 ground wire going back to the panel
Anywhere in the Grounding Electrode System - the bare wires connecting the panel to ground rods/water pipes/etc.

Then, change the receptacle to NEMA 14-30 type and hook up ground.   If the old neutral wire is bare, insulate it thoroughly.  Shrink tubing is not excessive. It mustn't touch ground.
POOR: Change cord to NEMA 10-30 ($15)
There is a procedure in your instructions to swap the dryer out for a 3-prong cord.  It involves changing the cord (obviously) but also involves adding a ground strap tying neutral to ground.  This instruction is telling you to &quot;bootleg ground&quot;, which is stupid and dangerous, and illegal anywhere but here because of a special exception notched into Code for dryers and ranges.  Ugh.
The problem with this procedure is that if the neutral wire breaks, it will electrify the chassis of your dryer.  The reasoning behind the exception to the rule is that &quot;Dryers are unplugged rarely, and this isn't likely to happen&quot;. This was installed due to pressure from appliance manufacturers, who were scared of losing sales if rewiring was required.  The &quot;retrofit ground&quot; option wasn't available then; it's a quite recent development.
LESS POOR, BUT ILLEGAL: Cheat a separate ground. ($20)
Defy its instructions, don't attach the ground-neutral strap, and hang a ground anywhere you can, in some way which is inferior to the Retrofit Ground procedure (which presumably, you are unable to do).
You could do it all neat and proper, like a retrofit ground, but don't. Deliberately make it look horky-dorky.  That way nobody mistakes it for a proper, legal retrofit ground.
Of course, this is very naughty.