With the Blu-ray Disc Players currently on the market, as soon as you connect the Blu-ray Disc Player to your HDTV or video projector, and turn both units on (set the TV to the input you have the Blu-ray Disc Player connected to), the Blu-ray Disc Player will automatically adjust to the native resolution capabilities of your HDTV or video projector.
In other words, a Blu-ray Disc Player knows what it is connected to and what type of connection you are using (HDMI, DVI, or Component). If it doesn't sense a 1080p input, it will set itself to whatever the native resolution of the set is - whether it be 1080i, 720p, etc... Afterwards, you can still go into the Blu-ray Disc Player setup menu and make any additional changes you choose (if you prefer 1080i, 720p, etc..).
Also, the maximum resolution that a Blu-ray disc player can output via Component (red, green, blue) is 1080i, however, that has now changed for Blu-ray Disc players made after January 1, 2011.
In addition, if you are using HDMI, HDMI/DVI or Component video connections, and you have an HDTV or video projector with 720p native resolution, instead of 1080i or 1080p, I have found that if you manually set the Blu-ray Disc player to 1080i, the image looks slightly better. This may be due to the fact that the Blu-ray Discs themselves are mastered at 1080p, and it appears that is easier for the Blu-ray disc player to scale down to output a 1080i signal than a 720p signal, since 1080i is closer to 1080p than 720p. Of course, the other explanation is that some Blu-ray Disc Players may just not have very good built-in 720p scaling capability.
Check your user manual if you suspect any variations to the above information.
NOTE: By the end of 2013, all analog video connections (composite, S-video, and Component) will be eliminated as connection options on all new Blu-ray Disc players manufactured for the U.S. market. Some manufacturers have already started this process during 2012. Analog audio connections are not affected - they will still be able to be included, at each manufacturer's discretion.
If you have a home theater receiver that has HDMI inputs and the receiver has Dolby TrueHD and DTS-HD Master Audio decoding (check the labels on your receiver or the user manual for details), your home theater receiver would be able to accept either an undecoded or fully decoded uncompressed digital audio signal from the Blu-ray Disc player via the HDMI connection. This is the preferred connection to use.
However, if you have an older home theater receiver that does not have HDMI inputs, or one that has HDMI inputs that only pass through video and audio to your TV, then it would be best to use the traditional method of connecting the digital audio outputs (either optical or coaxial) of the player to your AV receiver. Using this connection you would be able to access all undecoded audio signals from the Blu-ray Disc player (the receiver will decode them) except for Dolby TrueHD, DTS-HD Master Audio, or multi-channel uncompressed audio.
On the other hand, if you have a set of 5.1 or 7.1 channel direct analog inputs on your receiver and your Blu-ray Disc player has a set of 5.1 or 7.1 channel analog outputs, this is a better option than using the standard digital audio (optical or coaxial) connection option as the 5.1 channel analog outputs of the Blu-ray disc player can decoded the surround sound signal internally and pass it to your home theater receiver as a fully-decoded or uncompressed audio signal that would be the same quality as using the HDMI connection option for audio. The downside is that instead of connecting one cable to your receiver for audio, you would have to connect five or seven connections to get the audio from your Blu-ray Disc player to your home theater receiver.
Check out a photo of the type of audio and video connections that you might find on a Blu-ray Disc player and match them to what you have on your player.
Also, for an even more detailed look on how to access audio from a Blu-ray Disc player, check out my article: Five Ways to Access Audio From a Blu-ray Disc Player.
In addition, if you have a 3D TV and 3D Blu-ray Disc player, but your home theater receiver is not 3D compatible - I have some additional connection and setup tips in my article: How to Connect a 3D Blu-ray Disc Player to a non-3D Home Theater Receiver
After connecting all of your audio and video connections, also consult your Blu-ray Disc player's user manual for any additional audio and video setup procedures.