duct sealing
All types of ducts – sheet metal, flexible and rigid fiberglass duct board… - are prone to air leaks, particularly the most common type of ducts: sheet metal...
Duct inspection
You may start with a visual inspection of your ducts. You may look for disconnected components and leaks in the connections and joints between the ductwork and the air handling unit and the plenums...
Professional tests
But to test the airtighness of your ducts, and to fully assess their leakage problems, you need a 1) special fan and test called blower test door or a 2) specific duct blower test.
The test is required by some Energy Efficiency Incentive Programs (Energy Star Programs, for instance), and is also performed by some contractors for a very low fee or as part of a bid to seal ductwork. Professional tests will take about an hour.
Duct Sealing materials
Use duct sealant (mastic) to seal the seams and connections of ducts. In some cases, some tapes (metal-backed foil tape, for instance, may also be used). Common duct tape is a bad option, that you should avoid.
See:
Duct Sealing Materials: Mastic.
Duct tapes
What to Seal
Basically you need to seal the openings in the air handler units, the register boot, the joints where ducts of different shapes meet, and alls seams and connections between the different parts of the ducts.
Seams in the air handling unit, plenums and rectangular ductwork should be carefully and properly sealed. Pay special attention to hard to reach places, and disconnected parts.
Other Leaky Areas
Ductwork located in the living space (including the air handler) isn’t a first priority in terms of air sealing, and usually doesn't need to be insulated.
Only drywall-to-ductwork and other similar connections to unheated areas have to be sealed.
Sheet Metal Ducts
Sheet metal ducts – the most common type of ducts - have more connections and joints than flexible ducts, and are largely used both on return and supply parts. All their seams, joints and connections have potential leakage and should be properly sealed.
Many of these ducts aren’t sealed during construction, making sealing during installation more pertinent. Use mastic to get a superior sealing, and screws to fasten the joints.
This type of ducts should be insulated when located in unconditioned spaces.
Image credit: DOE
Flex Duct / Flexible Non-metallic Ducts
Flexible non-metallic ducts are factory-insulated and have few joints and connections and, consequently, low leakage potential. They are used as return ducts, and also in run-outs/curved surfaces (in this case with metal collars bridging the flexible duct to supply trunks, branches and plenums often made from duct board or sheet metal).
Though they have low leakage potential, they are easily crushed, torn or otherwise damaged during installation. For this reason installation is often more important than sealing. Pay attention to installation and to the possible damages associated to it. Sealing should be done with mastic.

Fiberglass duct boards
Fiberglass duct boards are factory-insulated and sealed. Connections should be fastened and sealed with mastic (or approved tapes).
See also: Air sealing the duct air handler, plenums, boots and elbows.
See also:
Duct insulation and sealing basics
Duct Insulation
Sealing the Duct Air Handler, Boots and elbows
Duct design, sizing and installation
Duct Mastic
Duct Tapes
Duct fasteners
Pipe insulation
Insulation basics
