The Internet has, of course, eclipsed print advertising for most purposes. It can be much less expensive and reach more people, but the competition has become imense.
Birth mothers today are much more likely to search the web than they are to look in a local newspaper.
There are essentially two different approaches to internet advertising. The first is to develope your own web site and fight the search engine battles to be found. This is not easy and requires a significant level of expertise. It also requires a great deal of dedication. Prospective adoptive parents should ask themselves if they are up to the task. If you possess the time and energy to do this, it is a good approach. But it is not likely to be effective if undertaken half way.
The other approach is to list with an existing site which publishes profiles of adoptive families, so that a birth mother may scan many of them in deciding who, if anyone, she wants to contact. There are many such sites. Perhaps the largest and best known is ParentProfiles.com They have claimed that 50% of those who list with them are chosen within a period of one year. If true, that is a high success rate. They do require that there be a completed Home Study and that anyone listing with them have an adoption attorney on retainer who can certify that they meet all adoption requirements of their home state.