How can I make a BBQ sauce from my dry rub?
You haven't given us much information to go on here, but I'm assuming your dry rub is a mixture of dried spices and possibly sugar.

If that's the case, I would fry some onions and garlic and add the spices (not the sugar, which will burn) to them while they soften. Then I would add the usual BBQ sauce staples - ketchup, vinegar, some water, and the sugar before simmering for a while to reduce and thicken. Put through a blender and sieve and you're good to go - if your spice rub is distinctive enough, it should translate through into a sauce well.

If there is a particular flavour that makes your dry rub stand out, you could add another 'version' of it to the sauce to emphasise it - for example, if you have fennel seeds in your rub, you could add a shot of aniseed liqueur like Pernod to the sauce, or if you have orange zest in the rub, use orange juice instead of water.