If you have NO IDEA what you're doing, where to start, what is safe/unsafe, or want some general direction.. Then, yes. A PT cam get you on a program for your goals and teach you to do it safely.
Be advised you DO NOT need a PT for life and you do not need a PT after you are comfortable with your self and routine. To add something more, go get a few appointments and tell them you need a change.
In the end, NO, unless the above sounds like you. You can also research the crap out of this and figure it all out yourself too, but that is no fun if you're new to it all. Most gyms hire qualified staff so you should be fine. GOOD LUCK!
No. Absolutely not. What is important, as waverider stated, is to learn the proper forms of exercise. There is a proper way to do a push-up, pull-ups, sit-ups and to lift weights. Weight lifting especially is an area where you need someone to show you the best way to lift. It is helpful to have someone who is experienced demonstrate and guide you at the beginning.
What you MUST do if you don't want to see a personal trainer is buy a book on training exercise another thing to do is go online and subscribe to Men's Health. It's VERY important to learn the proper forms when you exercise so as not to injure yourself. Make sure to check with your doctor first and get his/her OK.