Welcome to the world of Mac!
Program files you download often end in
.dmg (disk image), such as install
flash_player_osxub.dmg for (US version) Adobe Flash Reader
Unless you've specified otherwise, downloads usually are saved in the Downloads folder.
Double-click on the Finder icon (far left in the Dock) and navigate to the Downloads folder.
In the Places column of finder double-click on the folder that has your username. It should have an icon that looks like a house.
The 'Downloads' folder should be located below the 'Documents' folder.
Double-click on the 'Downloads' folder
Locate the desired .dmg file. You can sort the columns by clicking on the column header.
Once you've located the desired .dmg file, double-click on the filename to install it.
(Flash Player installer opens another window with a file that ends in .pkg and has an icon that looks like a cardboard box.) Double-click on the .pkg file
Depending on the program, you may need to then confirm that you want to install the file, agree to various terms and conditions and/or drag the application icon into the Applications folder.
Depending upon how System Preferences are set, you may be asked to enter your user password, if you require a password to sign on to your user identity.