A hand phaser is essentially a phaser pistol. Various models have appeared in Star Trek through the years.
TOS Hand Phasers
In the original Star Trek, the Federation has two types of hand phaser. "Phaser 1" is a small oblong device with an emitter on one end and fire controls on one of its largest surfaces. These controls include a firing button, a dial to change the setting, and a crystal meter, presumably for reading either the setting or the charge status or both. While such a weapon would not be easy to aim at any significant range, it is readily concealable.
"Phaser 2" is actually an attachment for Phaser 1. The device consists of a conventional handle and trigger arrangement (although shamefully lacking a trigger guard) with a larger beam emitter at the end and a niche on top into which a Phaser 1 fits. Presumably the Phaser 1's firing button is disabled when it is attached to a Phaser 2 handgrip, while the meter and adjustment dial function normally for the combined weapon. The Phaser 2 attachment also has a dial at the back which presumably allows the user to adjust the spread of the beam, a feature not seen on Phaser 1. Phaser 2 increases the power output of the weapon, and the combined device probably has greater energy reserves.
Phaser 2 and at least some earlier models of hand phaser have an overload function of dubious value. By setting the phaser to overload, the user can turn it into a makeshift bomb with enough explosive power to seriously damage a starship if it detonates inside. It takes a minute or so for the overload to build up to detonation, and it can be stopped as easily as it is started. The purpose of this function is unknown: it has little, if any, utility on a battlefield, and it gives any disgruntled crewmember with access to a phaser the ability to seriously harm the ship. It would allow the user to use the phaser as a demolition charge, but in most situations, it seems that the user could just shoot the object they want to demolish. Starfleet seems to just like designing devices with built-in self-destruct features.
TNG Hand Phasers
The TNG-era Phaser 1 is not substantially different from its 23rd-century ancestor. It has a firing button, two buttons for adjusting the setting, and an LED meter for reading the current setting. It is even smaller and more concealable than the earlier version.
The 24th-century Phaser 2 is not a Phaser 1 attachment like the earlier model but an entirely independent weapon. For handling and aiming purposes, this weapon is an ergonomic nightmare: it's handle is angled oddly, and it has neither sights nor a guard for its trigger button. It is, however, something of a Swiss army knife, having sixteen power settings and a variety of beam adjustments that can be used to disrupt force fields or repel "firestorms", among other exotic applications.
The 24th-century Phaser 2 includes a self-destruct feature; there is no indication that Phaser 1 has one.
Hand phasers are oddly sensitive to local environmental conditions. Radiation, in particular, seems to negatively affect them. A TOS-era hand phaser once failed after being close to a 20th-century nuclear reactor for a short time, and TNG-era hand phasers are known to be non-functional in the presence of "hyperonic radiation", whatever that is. "Energy dampening fields" also make conventional phasers useless, presumably by design. "Regenerative phasers" were eventually developed to mitigate some of the problems with using phasers in adverse environments.
Hand phasers are widely considered ergonomic disasters, since they lack trigger guards or proper sights. Many TNG-era phaser designs are actually worse than their TOS ancestors in this regard. It's possible that -- in typical Federation over-engineering fashion -- they use some kind of sensor system to verify that the weapon is being held correctly instead of a simple trigger guard, but no mention has ever been made of such a safety feature.