How do I send verification mail from my drupal custom module?
I am not sure about what kind of verification emails you are sending, though I believe if you peep inside drupal core user module you can get hold of function which does the same,as for user registration process we have email verification option also.

A very simple straight custom way might go in the following way


How you will be generating the verification code?

while sending the email create a link something like www.mydomain.com/email-verification/%random_string%

Create a custom table with column as email,random_string,verified
once you have generated it, make a db query to insert the link you created a point back against the email user entered and set verified to 0 in the custom table.
send the email
In your custom module implement hook_menu() with menu entry fir "email-verification" .
In the page callback using wild card check if the random_string exists in you custom table, if so set verified to 1


Not exact but close to what you may need.

Update:

global $base_url;
$random_string = substr(str_shuffle(md5(time())),0,10);
// Link 
$email_link = $base_url . "/email-verification/" . $random_string;