A shield is a board that can be mounted on top of the Arduino board. The shield pins are inserted into the sockets located down both sides of the Arduino board. Because the Arduino is an Open Source Hardware Design there is wide range of low cost shields available from multiple suppliers.
Shields can be stacked on top of other shields. However there can be physical mounting issues with some shields which can limit the stacking of some shields. You all also need to be careful of the amount of power that is required by some shields. The Arduino USB is only rated at 500ma.
When stacking shields you need to consider what pins are in use. For example if the I2C or SPI bus is in use by a sensor on one shield then those pins can not be used as input / outputs on another shield.
Most shields come with the headers installed (soldered to the board). However some boards do not and you will need to install the headers to suite your requirements. This will involve soldering. The arrangement of headers depends on what version of the Arduino board you are using.
You can use ether a straight male header or a stackable header. If the shield is not going to have another shield stacked on it then use a straight male header. You will need to use a stackable header to mount additional shields on top.
The easiest way to solder the stackable header onto a shield is to use an existing shield, turn it upside down and mount the headers onto that.
Slip the new shield onto the headers and solder away. Note that the new shield should be mounted upside down as well.
It is a good idea to just solder on the end pins of each header. Carefully remove the board and check that the headers are vertical and not angled. Also check that the header is sitting flat on the shield. If happy with the placement then solder the remaining pins on each header.
Likewise for a male header you can use an Arduino board to hold the header while you solder on the shield
Once all of the male headers have been inserted into the Arduino board you can then slip the shield on top.
It might be a good idea if you have not done this before to just solder the pins at each end of the header. Carefully lift of the board with the new headers and check for orientation. Its a lot easy to desolder two pins instead of 8.