In my experience, using actual ASL is better than employing "baby sign". Just like with spoken language, they come up with their own versions of certain words, they will automatically do the same with ASL and you will still understand if you are tuned in. Those who choose "baby sign" tend to learn a few words and stop before they've really tapped into all the benefits there are to offer in signing with your child.
ASL is pretty easy to learn because most of the signs make sense. Even those that don't make sense at first, usually do when you learn their origins. The color "black" is signed by drawing your index finger across your forehead. When it was explained that one of the few jobs a deaf person could have back when ASL was being developed, was coal miner, suddenly the idea of drawing a line across the base of the helmet wear the black color of the coal dust would end and the color of the miner's skin begin made the sign make sense. This makes words easy to remember once you've learned them and start using those signs. An example of an easy to understand sign is "milk" it looks a lot like the hand motion made by someone milking a cow.
If you decide to do Signing with your child while you are still pregnant you've bought yourself time to learn a few things (and teach those to other care givers and siblings) before baby comes along, but if baby is already here it is no big deal, just start as soon as possible for the most benefit. I suggest choosing two-three signs to learn along with 5 letters of the alphabet each week after you've made the decision. This way you don't overwhelm yourself at a time in life that is pretty overwhelming anyway.
There are classes you can take your baby to in some locations that teach baby sign. I've seen new mothers frustrated by the fact that such classes aren't available in their area, but PLEASE don't let this frustrate you. Honestly, what new mom really needs the burden of ANOTHER item in their schedule? Plus, waiting for when you can get to such a class and baby can participate it starts you off later than just getting going on your own will. Start on your own with the wonderful plethora of ASL resources out there. There are always a few ASL dictionaries available at the bookstores (and online). Better yet is ASLpro (link below), which is free and kept up-to-date and the movies available that you can watch with your child. At the same time, if your child is 9 months and you want to get started, there is nothing wrong with that either. If you have a little one that is a late speaker I would still personally recommend signing as a way to help him or her have SOME way to communicate with you, but I would suggest you proceed with the knowledge of your child's speech therapist.
Start using signs consistently every time you say the word that goes with it, as soon as you know the sign that goes with the word you are using. While you can expect a response too soon, you CAN'T start using it around baby too soon. Babies can't sign until they are ready and a number of developmental milestones must first be met, both physical and mental. However, you never do know when that moment will come that they will start to be able to notice, and notice patterns. Start as early as you possibly can. If baby is around already, he or she will see you signing and hear the words together from the moment he or she is able to notice and the association will be strongest for him or her. Using ASL as often as you can simply gets you into the habit and makes it harder for you to NOT remember the words you are trying to learn.
This method is what worked well for us and I know to have worked for others. Babies are driven by needs, so I suggest the first words you learn are about needs, then a couple of favorite people and toys. Food, Milk, More, All Done, Wet, Mommy, Daddy. . . THEN add, ball, doll, bear, blanket . . .
The reason I suggest the alphabet, is mainly for you - not so you can teach it to your little one (though it isn't a bad idea to do the signs along with the alphabet song should you sing it to your child). Many signs use a letter as part of the sign. Knowing the alphabet will help you to better understand and remember these signs. For example, Family uses an F and People uses a P, but the movement of the hands is the same.
I suggest learning a few of your favorite nursery rhymes or songs in sign too. We did "Baa, Baa, Black Sheep" and "The More We Get Together", quite a bit in the beginning. More songs came later. As your child develops, and he or she gets "needs" words under his or her belt, more "interest" words will follow and song can often be a great way to keep the vocabulary additions rolling along. There is a wonderful colors song on "My Favorite Things" by Signing Times (link below). This series also has fabulous songs for fruits and veggies, different animals and all kinds of good stuff.
Feelings are the toughest to teach as they are the most abstract. Of these, the most useful and arguably a "need word" is the sign for pain (basically two index fingers pointing toward each-other and the area in pain while wearing a pained expression on one's face). These words are also some of the hardest spoken words to teach kids too. Use picture books about feelings for introducing these words and as you go about daily activities echo to your child, "are you feeling sad?" when he or she seems sad, "oh you look happy" etc. in spoken words while signing the emotion and they'll pick these words up too.
Baby Einstein has a couple of videos with ASL, but we found the "My Baby Can Talk" series (link below) much more engaging and useful for Alice. It is structured in very much the same way as the Einstein videos, but the signs chosen were much more useful. For example, the Einstein video gives signs for Window, refrigerator, computer, piano, and sofa while My Baby Can Talk gives the signs for cereal, crackers, please and thank you. The Einstein video had wonderful little clips with puppets Alice really liked, but no signing was done during these sections. We would play one video and watch it together one time each day.
When Alice got too old for these, we introduced, "Signing Time" which is much more geared for toddlers and school-aged kids with its up-beat music, humor and faster pace. For your own learning purposes ASLpro is a wonderful free resource recommended to me by a deaf friend when Alice was about six months old. I have referred to this site frequently. Once Alice started speaking fluently (and we moved away from the friend that used ASL regularly), it was difficult to keep up the ASL, however we do still remember bits of it and it does come in useful from time to time.