It really depends on the course, where you are, and how early you identify a red is coming for you.
The first thing to do is try and identify when it's coming for you as quick as possible. This is easier in local multiplayer than other modes, but the sooner you know it's coming, the sooner you can prepare to dodge it and plan how you're going to dodge it.
Let's look at all your options:
Protect yourself with items I know you specifically mentioned if you don't have an item, but thought I'd mention it to reinforce how strategic it is to always keep items until a good opportunity arises.
Hit someone else! One way to dodge it is to have it hit someone else! If someone's close to you, you can slow down, move to the side, etc. You obviously can't always do this, as it's pendant on other racers being close to you - but it is quite effective if you get it to work!
Have it hit an object Red turtle shells will break if it rams into a course object - such as a tree. If you're on a course with objects, try to get behind one of them so the red will smash into it - instead of you.
Have it miss you - Sharp Drifting strat If you are on a road with sharp turns, you can turn so sharply that the red will overshoot and miss you.
Here is the way to do it on a straight path, assuming no objects/racers are nearby:
dodge it This is a difficult thing to do. If you've ever played Mario Kart Double Dash, dodging reds is most similar to how they were dodged in that game. Basically, when it's about 2-3 seconds away from hitting you, do a sharp drift turn, followed by another sharp drift turn in the opposite direction. If you're just learning this strat, do it over and over again as soon as you hear the warning - as it's not the easiest to do.