There's little difference between the activity of searching for some missing object (find) and trying to locate that missing object (search for), so, as you note both imperative forms are fine:

[1a] Find Tommy. [1b] Search for Tommy.

The same goes for the infinitive:

[2a] It takes time to look for a good stone. [2b] It takes time to find a good stone.

Presumably you're looking for the right diamond for your fiancee's engagement ring.

The same also goes for the gerund:

[3a] Looking for a good stone takes a lot of time. [3b] Finding a good stone takes a lot of time.

But while you're looking for a specific object like your book, you aren't finding it. In fact, you may never find it. After you've found your book, you stop looking. So in these cases there isn't much opportunity for the progressive form of the verb to indicate a continuing activity, which is why

[4a] I am looking for my book.

sounds OK, but

[4b] I am finding my book.

doesn't.

But there's another connotation to the word find, and that's discovery. This can well be an ongoing process, and one suitable for the progressive form of the verb. Here's an example from Successful Single-Sex Classrooms (2010) by M Gurian, 鈥嶬 Stevens, 鈥巃nd P Daniels:

[5] I am finding that writing tends to be a chore for the boys.

This is particularly prevalent in touchy-feely self-help books in the locution "to find oneself," meaning to come to self-awareness. For example from Finding the Deep River Within (2007) by A Seixas:

[6] It feels as if I am finding myself again, coming home to myself.