First and foremost, you should determine if you truly like your professor or you are simply infatuated with him.
There is a difference and it can be very easy to get these two confused.
When you are infatuated with your professor, you may rarely think about what he may be like as a person.
Most of your focus would be on what he can do for you and how good he can make you feel.
In other words, you would be a lot more prone to focusing on the pleasurable aspects of being with him.
You don’t allow yourself to consider what he may do as a person that may not be particularly good.
You may not allow yourself to consider the possibility that he may have anger issues or he may have a lack of empathy for others.
This is often what happens when you are infatuated.
You are immediately blinded by what you consider to be perfection before you.
You are blinded by how good that perfection makes you feel whenever you think about him or you are in his class.
On the flip side, if you truly like him, you would be more cautious.
You would wonder what kind of person he is when he is not in a class setting. You would be curious about how he interacts with his friends and family.
You may even wonder if your friends and family would get along with his.
You would be concerned about how he has treated people in his previous romantic relationships.
Was he kind and attentive to them?
Was he giving of his time?
Was he trustworthy and faithful?
These are the kind of thoughts that would be most likely going through your mind when you truly like him as a person and are wondering what it would be like to date him.
You are not infatuated in this scenario.
You do think about the implications of his character.
You do consider what he may be like as a person outside the academic arena.
You wonder if you would both get along.
You wonder how you would both treat each other if a disagreement were to occur.
In other words, you really think things through before you allow yourself to get carried away by your emotions.
Now, this being said, if you have come to terms with what you are truly feeling, we can proceed.
If you are merely infatuated with him, you may want to give this more time.
Infatuations can flame out quite quickly because they normally have no real foundation to begin with.
If your infatuation persists however, there may be something more to this.
This is where you may be actually looking at this professor as something more than eye candy.
This is when you can act.
Your best option would be to get him outside the class environment.
Start conversations with him after class and learn about what he loves to do or where he tends to go on the weekends.
Use this information as your guide.
If he tells you that he loves theater, you can learn more about theater on your personal time so that the next time you see him, you will have something more to say about it.
This creates a connection with him.
This kind of connection is what will begin to draw him towards you and even have him looking to talk to you more often after class.
From here, he just may tell you about the next theater show that he intends to attend. This is when it would be most natural for you to accept the invite or even invite yourself.
Outside of the academic environment, he may be more open in discussion and this could possibly lead to future romantic dates with him.
Hence, your goal should be to meet with him as much as possible outside of the classroom environment.