Proteins form as chains of peptides that fold up. Denturing the protein is the same as unfolding it.
The folds in the protein are held by electrostatic (i.e. Hydrogen) bonds, so increased pressure and temperature can provide sufficient free energy to knock the folding apart. The Ph can affect the relative electrostatic forces between the peptides and change the relative energy states of the protein.
Chemical and cold denaturing are probably more complicated.
I hate to give you a link, but the topic of protein stability is not something which is easily broken down into a paragraph or two. It's a bit old, but still covers the essentials of the topic succinctly.
In general, thermodynamics of the folded state versus the unfolded states will be a major determinant in whether or not a protein denatures. If one can overcome the hydrophobic interaction and various electrostatic/hydrogen bonding interactions, the protein will denature. The mechanism of cold denaturation has also been of increasing study, and a somewhat intuitive way to think about that is to consider that the colder the environment gets, the protein is sort of a "heat source" and it denatures as its energy is sucked out into the environment. This is hardly rigorous and even a bit misleading, and I would shudder at even describing it this way but it's not the easiest topic to describe in this sort of format. Chemical denaturation is typically taken to mean a reduction of a protein, where sulfide bridges are broken. While proteins can actually degrade via chemical methods, it's not the same as simply losing its fold. Detergents can also get a protein to unfold, surrounding hydrophobic regions with their long hydrocarbon tails and exposing their polar head group to the (typically) aqueous solvent.
The thing to remember is that protein folding is still something of a mystery - its reverse process is still something shaded in mystery, although we are gradually peeling back the veil.
Let me first state that I'm no expert.
I'v been a paramedic for the last 28 years. Every year, we respond to two or three 'Heat Stroke' related calls. In my study of this contition, I have learned that when the internal body temperature raises above 105 dF, the protiens in the nerve tissue in the Hypothalmus, denature and permanently break down. This prevents the Hypothalmus (our internal thermostat) from nerologically doing it's job. This is serious because there is almost a 0% survivability rate with this.