I Have A Two Way Switch At The Top Of My Stairs Leading To The Basement & A Two Way At The Bottom Of The Stairs In The Basement.. They Are Connected With A #8 Wire I Think.. Round Wire With A Blk,White & Red.. I Was Doing Renovations & I Pulled The Wires Of The Switch In The Basement & Now It Does Not Work Right.. The Switch Up Top Was Not Touched.. It Has 3 Terminals For The Blk,White & Red Wires.. The Switch Below Has 3 Terminals As Will,But There Is The 3 Wires From The Top Switch Going Into The Box Along With A Blk & Red Wire From The Light.. Just Wondering How To Connect The Wires In The Bottom Switch So That It Will Function Right.. The Light Is Suppose To Turn On Or Off With Either Switch, But Right Now It Is Not doing That.. Hoping U Can Help.. Thanks.

Look at the switch. You will see that two of the terminals are one color and the third is another. The two terminals that are the same color are called travelers. The terminal that is the other color is called the common. It is probably also marked "common".

Connect the same wires that are connected to the travelers at the top of the stairs, to the travelers at the bottom of the stairs. Connect the remaining wire to the common.

Most of us know this as a 3 way switch. http://www.wfu.edu/~matthews/courses/p230/switches/3way/variations.html

Are you located in the USA?

This works no matter the method of wiring, or colors of wires, and is quick.
Remove all wires from both switches, keep wires clear, turn power back on.
1 of the 6 wires will have power, this connects to the common of the first switch(silver screw), the other 2(travellers) connect to the 2 dark screws.
Go the other switch location and see which of the 3 wires is hot, identify it, turn first switch to there position and see what other wire is now hot at second switch location and identify this as well, these 2 are your travellers and connect to the two dark(same colored) screws, the remaining wire connects to the common of the second switch and this is the wire that goes to your lights.