Your eight-month-old is developing in a unique way. That is to say that while there are "typical eight month things" you can look for, it's still wise to realize that each baby is developing at his own pace. For instance, one baby may have four teeth by now, while another has none. One may be crawling and even pulling himself up while another is still happy to roll around. Your baby may even skip crawling altogether and find other different ways of travel (such as scooting along, while sitting on his bottom -- you just never know!).
But whatever the case, by all means, be sure your house is childproofed by now! Move all cleaning products, poisons, and other hazardous materials out-of-reach of baby. Look around on the floor regularly to ensure that no small items are lying around, which he could choke on. He is at a curious age, and will tend to put anything and everything in his mouth. It's up to mom and dad to keep him from putting the wrong things in his mouth since he sure can't think for himself. Those items must stay out-of-reach! However, when it comes to items that are safe for him to touch but you just don't want him to (dvd cases for example), you can train him not to bother them.
Even though babies are developing at different rates, the chances are that your baby is quite mobile by now. Most babies have started to crawl at this point. My guess is that your little guy is getting into everything! He's probably developed a good deal of strength in his arms and legs, and is now really putting that to use! He can be quick too: he might be across the room from you one moment, and then right at your feet the next! Keep your eyes open so that he doesn't disappear from the room or fall down the stairs (which is where a baby gate may come in handy)!
"The pincer grasp", that is, using the thumb and a finger, is developed by now and is useful for picking up rather small objects. For some eight month old babies, this comes in handy at mealtime. Other babies at this age may still not have teeth yet, and they are happy to be spoon fed with pureed baby food. If your baby is ready for finger foods, however, these might include bananas, pasta, toast, well-cooked meat (which has been cut-up-extremely-small), etc. Avoid foods that would be a choking hazard to your baby, such as hot dogs, raw vegetables, raisins, etc. And, of course, never leave your baby unattended when he is eating. In either case--finger food or pureed-- all babies at this age must continue to drink breast milk or formula very regularly throughout the day.
Nothing much has changed in the sleeping department. Fact is, babies are growing and need lots of sleep! Your little sleeper is probably averaging 13 to 14 hours a day. Let him get in a morning nap and an afternoon nap, if that's what he needs. Naps vary: while an hour or so nap is expected, your baby might get along with a few little short naps. Also, if your baby is teething, this could change his sleeping pattern temporarily.
Someone is really having fun discovering his vocal cords! You may be hearing lots of sounds of "ma-ma" and "da-da" whether they were intended for anyone or not. And don't be surprised if he is screeching just-for-fun! He is discovering the noises he can make, and once onto something, he may do it again and again and again! It's really cute, actually. It's a good idea to read to him regularly, pointing to objects in his books and saying what they are. It's always good to talk (and to sing) to your baby. By now, he can understand a few simple words, especially if you are saying them often. These words might include "bye-bye", "milk", and "no".