I know that water with salts is a good conductor-However wetting a hand only adds water to a not very conductive surface. How does water actually reduce the resistance of skin? The way I am seeing it is that as opposed to just a wire touching skin, the wire is touching water then touching skin, which still does not seem to imply we would have less resistance.
First of all, don't try this at home.
You may consider your body as a resistive element (with total resistance about 1000 Ohms). This depends on personal parameters, given voltage and many other factors, but let's say it's around that. It is your total (equivalent) resistance, but each part of body has it's own, but combining them together will lead to this ca. 1 kOhm.
If you touch a wire, the current flows through the body. There is a voltage drop on it, so you calculate current dividing voltage by your body, if you are still able to ;-).
When you are wet, water makes a surface on your skin. This is equivalent to connect your body with this water surface in parallel. The total resistance of your body and water connected in parallel is smaller, but current through the body itself does not change, but it is larger in total as some flows through water. Some electricians still believe that keeping hand in pocket while touching a wire with the other hand, in case of failure, will make current flow through the hand in pocket and bypassing the heart. This is very hard to prove, however.
For example, let's consider you have wet arm from fingers to a shoulder. If it is wet, you add water in parallel and thus lower resistance of arm. So shoulder has higher potential than it would had in case of dry arm. This means that larger current flows through your heart.
Current can in some part lower body resistance: because water tends to flow under your skin, which is not a solid barrier. This might be because of energy of the flowing current, increasing the temperature, and making some dielectric phenomena on the cellular level, that destroy skin surface.
All these things apply to some high voltage, say 200 V and more. If you touch 24 V with a wet hand, you probably will not see the difference.
To read more about human body resistivity, you might like to read this article. Please notice (Table 1) that fat has much larger resistivity than other organs. Your skin has always fat on it and it is used by criminal police to find fingerprints. If it is wet, the fat surface could be thinner.
Salt water conducts electricity because it has mobile electrons and ionic states via the salt atoms, and dry protein of your skin is an insulator which has less reactive molecules than salt ions. Salt water provides a large surface area of contact for the conductive element and it connects with the sweat glands so electricity can flow past the skin and into your body, which has low electrical resistance.