I have a tv remote that I want to connect to an Arduino so that I can send a series of commands to the TV using the remote. I would like to open the remote and solder transistors or a Transistor Array in place of the buttons. I have never done this before, so what do I need to be aware of? I think that I will need to power the remote using the Arduino's power supply, but I am a bit foggy on the details.
If you're just running lines to the buttons, you won't need to power the remote from the arduino. You could just let it keep the internal batteries. But it would be possible to wire it up for power as well.
As a learning project, you could just take it apart and see if you can access the button contacts. See if the contacts are split. If so, shorting one side to the other should count as a button press. But the details have nothing to do with an arduino. They would depend on your specific remote and how it's constructed.
If your purpose is really to control the TV (rather than learning about the remote and fiddling with it), it will be much easier (and probably cheaper) to blast the IR without involving the remote at all. A single IR transmitter and a library would work in most cases. As an example: http://www.righto.com/2009/08/multi-protocol-infrared-remote-library.html
P.S. By coincidence, Adafruit just posted an updated guide to IR library use on Arduino. https://learn.adafruit.com/using-an-infrared-library/overview
Using an IR library as mentioned in a previous answer is likely to be about the best approach. However, if you decide to use electronic switches to jumper across the remote's switch contacts, consider using CMOS analog switch chips for the purpose. If each button on the remote connects one contact to a common net, inexpensive chips like 74HC4051 and CD74HCT4067 would serve for 8 or 16 buttons each, respectively.
I don't have a reference for an affordable many-SPST-contacts CMOS switch. Inexpensive chips with a few such contacts are available. The 74HC4053, for example, contains three SPDT CMOS switches. Handling a dozen buttons would use four 4053 chips. A CD4007 probably could provide three SPST switches also.
Edit: The figure above shows pinouts of CD4051/52/53 devices. To use a CD4053 as three separate switches, connect V- and GND to Arduino ground, V+ to +5V or +3.3V, and each of COMA,B,C to one circuit contact to be switched. With NCA, NCB, NCC connected to the other contacts of circuits A, B, C, raise ADDA, B, or C and drop INH to close circuit A, B, or C.
If your remote has dozens of buttons, it's likely that they are arranged in rows and columns for multiplexed scanning. In this case, follow the printed circuit tracks to identify which buttons attach to which rows and which columns. Suppose there are eight or fewer of one or the other; eg, suppose there are 5 columns and 8 rows. In this case, you would hook up 5 CD4051 chips: connect V- and GND to Arduino ground, V+ to +5V or +3.3V, and the COM of each 4051 to a different column line. Connect NO0–7 to row lines 0 to 7.
To close circuit j in column k, put j in binary on ADDA,B,C of all 4051s and drop INH on 4051 #k. (Either use one DIO line per INH, or use a DM74LS138 or MM74HC138 (etc.) and put k in binary on the A,B,C select lines of the '138.)