That's something that's hard to explain...
1) The guy from GTA 3 (Liberty City) is named Tofi, not Tommy.
2) Liberty City consists of 3 islands and is based on New York City during the year 2001.
Vice City consists of 4 islands and is based on Miami, Florida in the 80's.
San Andreas consists of 3 islands and is based on the state of California during the early 90's.
3) In a mission called "Farewell, My Love" one of your girlfriends named Catalina breaks up with you and goes out with Tofi (the same GTA 3 dude). In GTA 3, Tofi kills Catalina for some reason (I forgot why).
4) Ken Rosenburg is a lawyer who showed you (Tommy Vercetti) around in Vice City. Ken Rosenburg was in a lot of missions in Vice City (during the 80's).
Because of Ken's drug problem, he was sent to rehab after the end of the Vice City game. When he was released from rehab, all of the sudden he found himself as a Neutral Mafia Party running a casino that has tons of money.
Ken (Rosie) was surprisingly chosen to run this casino in Las Venturas because the 3 mobs who run the town couldn't trust each other to do it. You find this out very late in the San Andreas game, during a mission when you pick up the producer of a popular band that used to be in Vice City. This producer is named Paul, and his friend is Maccer.
4) There are many secrets and easter eggs in the game that include stuff from other GTA games, such as Tommy Vercetti and Lance Vance dolls inside Zero's RC Shop; and Vice City maps at the bottom of trash cans. Tofi (GTA 3 dude) is leaning on a car in the background of one of the missions (besides the racing missions in Red County), I forgot which mission he did that in.
5) Liberty City, Vice City, and San Andreas were all islands that the first original GTA game had. These current generation games are based on the early GTA games.
There are a bunch of links between the GTA games, and I'm sure that I
haven't explained all of them.
South Park, Charmed, Buffy The Vampire Slayer / Angel, Tru Calling, Family Guy, TrippingTheRift, FreeForAll, Futurama, Jackass, Lost, That 70's Show, Celebrity Deathmatch