First of all, I assume we are talking about a 2D game in which your objects are sprites, right? -- (because otherwise you wouldn't be talking about pixels).
So, yeah, use floats for position values like Cornstalks says above.
But what game framework or library are you using? Does it support drawing with subpixel accuracy? If not you have to round to the nearest pixel ... this tends to look jerky imho though. Basically do all your logic/updates in terms of floating point values and convert to the nearest pixel just before blitting. Or switch to a 2D framework that lets you draw to float locations.
Move it using the frame time of your function.
That means that you multiply your speed variables by the frame time of your window. Since time is constant, it will move at the same speed on everyones screen.
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When you place your object just cast the float to an int. When you cast it the decimal part will be ignored. So you can round it first if you wish, then anything over .5 should be +1.
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Yes, its 2D I am using SDL. okay looks like
