Saigon, with Hanoi, is one of vietnam's main entry points. There is an international airport 4-5 miles from District 1. You may get there on a taxi. If I am not wrong, there is a fixed price to get to the airport. If not, ask how much it will cost you before stepping in.
To enter Vietnam you will need a visa. You will have to apply for a tourist visa in your home country. If there is no Vietnamese Embassy, you will have to contact the nearest Embassy. If you are traveling around Southeast Asia, Bangkok is the best place to apply for a visa.
Tourists visas are stamped at the airport, and are valid for one month. If you want to stay longer you will have to apply for a visa extension. Any travel agency, or even your hotel, can do it. If you need to do any official paperwork, I also recommend you to do it through a travel agency (or through your hotel).