You say you have names but do you have places? That's probably the most important bit. Without at least a county you're unlikely to get far, although it still can be possible.
Next comes dates. I don't mean exact dates - just in general; e.g. if you're looking for your grandfather you must have a rough idea of when he was around. Similarly with other relatives.
Try roughing out a family tree in reverse order as below
, You
1960-
|
Father
1930-2000
|
grandfather
1900-1975
|
great gf
1870-1940
etc etc. And MOST IMPORTANT -- ASK EVERYONE FOR INFORMATION
Grannies, grand-dads, uncles, aunts, grannies friends etc etc. You'd be amazed what you can pick up.
Try that and then post some names dates places - even rough ones - you never know who may be able to help.
Best of luck
Jim