That is what i want to do. So its better with internet shield?
Well, that depends on a few things - your budget, and the amount of time you want to spend coding; an ethernet shield will most likely be more difficult to code for than a straight serial connection. However, a serial connection (via the USB cable) might be more difficult on the server end (it isn't as straightforward to do as you would think).
If you have an ethernet plug nearby, but your server is on the other side of the building, then that might be better? However, if your budget is tight, and you are going to put the PC in a locked cabinet, then maybe USB?
There's a lot of variables - some of which you haven't defined for us; so I really don't know which is necessarily best.
Do you know how to doo it? Or give me some tips?
To be honest, I've never done it, but the idea seems fairly easy. With the USB serial, you just need to set up communications between your server program and the Arduino over the serial port. This isn't as easy as you would think, but it can be done with some effort. For the server side of things, I would personally use Linux with a Perl or PHP program running as a CRON task or daemon that periodically polls the serial port, to see if there is a request waiting; if there is, then it would take the data, look it up in the MySQL DB, then based on the record data it returned, would send back a command to say "yes or no" to unlocking the door. The Arduino would then need to interpret that, and either open the doorstrike, or show an "error" message on the LCD (maybe with a buzzer or something?).
Its basically the same thing with an ethernet shield, except communications on the PC server side should be a little easier, but the comms on the Arduino side may become a little more difficult.
I actually have a project that I am working on that will do something similar - serial comms with the Arduino via PHP/Perl/Python; its a robot where a PC commands the Arduino (and gets telemetry data back for certain things) to tell the robot which wheels to move, which way to turn, control of servos for a pan/tilt system, and some other things (including a "heartbeat" so there is feedback in case the serial link is severed or rendered inoperable in some manner - the robot's weight will top 100 kg or more). I haven't gotten to this point yet (so many other things have gotten in the way, unfortunately - ugh).
I may not be able to help you, but there are tons of people out there and on this forum who have done serial communication and interfacing with PHP, MySQL, etc - with the Arduino. It's a fairly common task, so with some searching, you should be able to find enough information to hack your own system together.
Good luck - it sounds like a fun and useful project!