I started signing with my son at about six months. Someone had given us a video from Joseph Garcia about Baby Sign, and I watched it when he was about 3 months old. In the video, they recommended that parents start signing at six or seven months old, so that's when I started. I recorded his progress over time.
In my son's early language development (8 to 11 months), he acquired an equal number of words and signs. I found that the overlap between the words he spoke and the words that he signed was only 20% (I was expecting more). I also found that about half of his spoken words started with the letter B. (This makes sense because /b/ is easy to pronounce and is typically one of the sounds that babies master first.) Examples of his first spoken words were "Mama," "Baba" (the word we're using for Daddy), "baby," "ball," "bath," and "bye bye."
His signs were both functional ("all done," "eat") and also helped him to comment on things he observed in books, especially animals like "cat," and "dog" and in the environment like "airplane" and "train."
Examples of words that he both spoke and signed were "book," "cat,""more," "plane," and "up."
At 12 months, speech acquisition became more prominent and increased exponentially, whereas signs trailed off at about 14 months. Here's a graph showing his spoken and signed words over time.
So, from my experience, sign language did not hinder my son's speech at all. His rate of acquisition of spoken words was the same as signs and then speech became the preferred mode of communication. Of course, keep in mind that every child is different.
What I found was that sign language allowed my son to communicate about the world around him in ways that spoken language could not. For example, he would get so excited about motorcycles he would see driving by and helicopters in the sky. Both of these words were too difficult for him to say (or even attempt to say), but he could do the signs and 'tell' me all about it.
