What is the most appropriate rug for my living room?

I have a red leather living room set with black tables.

Without knowing the shade of red you have for your couch or what type of black the tables are (shiny, flat, wood, etc.), I would say go for a combo of rug/wall that will minimize the red of your couches. Often in black and white rooms, you can add a slash of red to liven things up a bit. However, in the case of a red couch, you have a large amount of color and need to work it into a neutral palette.

I'd go for a rug such as this Black and Red contemporary area rug that will still draw in your colors but isn't too bold. Alternately, you could choose an area rug such as this Black ash area rug if you like all black and prefer a luxurious shag area rug.  

With a room such as yours, I'd go for a feature wall that is bright and the rest of the room neutral. If you don't like white or off white for your walls, you could paint the entire room a light mocha or other light neutral. It will still work with your furniture, it just won't be as bold. If you don't mind white, you could put up some white/black wall paper on your feature wall in a striking pattern.

What is a good wall color for a living room with a white tile floor?

With a floor color like white, you can do almost any color. I'd focus on dark colors though, for at least one feature wall at least. Choose a chocolate brown on one wall and then a slightly lighter color on the other walls. You can put a great piece of artwork or family photos on the dark wall, and it will stand out against the floor.

Warm up your tile by adding area rugs. A warm, cozy shag would look great against white tile. Put something like this Cocoa Flokati on your floor. It  would look great with chocolate/taupe walls and dark brown wood coffee tables. 

Can you help with some ideas to decorate a rectangle living room?

Add a lot of color and a few differently shaped items to spice up your room.

If your room is a rectangle, focus on circular or rounded shapes. For example, a coffee table that has a curve like this would add some depth to a rectangle room.

When you have black and tan as your base, you are pretty free to add color where ever you see fit.  Put some bright red throw pillows on your couch. If red isn't your color, try a blue. Anything with a deep, vibrant tint will stand out.  Focus on different fabrics as well.

On your floor, add an area rug that has circular shapes such as this Funky Cream or this Dark Chocolate shag. A rug this color will contrast very well with your couch.

I'm not sure if you have windows in your room, but if you do you should add a curtain. Curtains always add a warmth to your room that bare windows are lacking.

If you can, grab an end table or two. Putting lamps on your end tables and surrounding your couch will make your room cozy. A vase with fresh flowers also adds a nice touch.