Correct camera setting for inside photoshoot?

Ok I have a Nikon D80 and have a white back drop and a light source plus my speedlight, do I shoot on P or should I shoot on manual setting, plus what should my iso be on. As sometimes my shots look grainy. I normally just have it on auto.

Not knowing the strength of your lights, one could not tell you what your settings should be other than manual. I would go no higher than 200 ISO.

Depends what lens you are using, the shoot you are doing, what you are shooting, what the "light source" is, what you are trying to accomplish…

there are too many variable…

go to www.strobist.com for information about this…

Should be in manual, shutter speed needs to be faster than 1/60 to avoid blur, aperture depends on what you are shooting, but if you set ISO to 100 or 200 and adjust aperture to get the shutter speed fast enough. If you shoot in RAW you can adjust the exposure slightly afterwards if needed.

Dude, way too many variables here. For one thing, your mixing lights. Don't use studio lights AND your flash on the camera. If the studio lights are the "light bulb" type, incandescent, they will be 1 color and your cameras flash will be another. One yellow, the other blue. Of course, maybe you WANT this effect, however, the camera's flash will totally over power the light bulbs unless you radically adjust your exposure.
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If your studio lights are flashes then you have to account for your cameras flash to be one of them flashes and adjust your exposure here as well, and this is only by going manual. However, the flash on your camera does not always give the best lighting for studio shots, if ever. However, again, maybe this IS the look your wanting to achieve.
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Have you read ANY of your owners manual? Have you read ANY book at all on photography or what it is your trying to do? Do you know what flash sync speed is? Do you know what it is for YOUR camera?
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Your trying to mix oil and water, apples n oranges here with wanting to use two types of lights. Pick ONE and stick with it till you half way understand what it is your doing.
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I wish cameras didn't have that stupid P setting. It make people even dumber. Learn M if you really want to get better pictures. Learn how your light meter works and where it's areas of sensitivity are. You have metering modes from a rather tight "spot" meter to matrix array for full area average. What are they for?
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You also have a digital camera. This means you can shot and look… Adjust "something". Shoot and look! You can keep this up all day for the cost of a couple batteries. However, if the camera is on P you will get the same mistake over and over and over… The sign of insanity is doing the same thing over and over yet expecting a change…
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Only by going manual will you ever understand what your camera is doing, how and why.
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At the moment ISO means nada here but to make you happy, pick a common film speed people had when cameras WERE manual and dinosaurs roamed the earth. Try 400…

What light source are you using - it needs to be colour balanced to your flash if you are using that at the same time. How are you triggering your speedlight?

ISO should always be as low as possible for image quality, but without knowing what the power of your lights are, its difficult to say. You should shoot on manual.

Are you trying to balance flash & ambient? It sounds like you have the gear but no idea. Suggest you read the Strobist blog & forget about using a continuous light;
http://strobist.blogspot.com/2006/02/welcome-to-strobist.html

I would suggest manual mode but everything else is dependent on the ambient light and the style you are going for.

If you don't know why oyur pics are grainy, then you need to read up on photography in gerenral.

In auto mode, the camera will set All yor settings in such a way as to have perfect exposure. One of these settings is ISO. ISO is how sensitive to light the sensor is. The lower the number, the less sensitive the sensor (and so the more light oyu need). The problem with increasing the sensitivity is that it adds digital noise to the image… Aka graininess.

Read up on exposure and how Aperture, Shutter Speed and ISO work together to expose the sensor.