Asymmetric DSL (ADSL) is the most common type of DSL sold by telephone and DSL companies. With Asymmetric DSL, the download speed is faster than the upload speed; hence it's not symmetric or, rather, it is asymmetric. With ADSL, you may be supplied with and asked to install filters between your telephone jacks and telephone devices in order to begin using your DSL service. The one shown in the picture here is one of the ones supplied by my old DSL provider. There are also versions that take the place of a standard telephone wall jack. The reason these are needed is that your DSL service and voice telephone service share the same pair of wires. (If your DSL provider provisions a separate pair of telephone wires for your DSL, you will not need these filters.)
A simple of explanation for what the filters do is that voice quality telephone service requires only about 4 KHz of bandwidth. That's only a small fraction of the bandwidth a copper telephone wire is capable of carrying. Therefore, it's possible to have both telephone and DSL service sharing the same pair of copper wires. The DSL modem is smart enough to ignore the signal below the bandwidth reserved for telephone conversation (plus a buffer of an extra few KHz to separate the two and prevent crosstalk). However, your old telephone equipment is not that smart, so the filters block everything but the very lowest frequencies - the frequencies reserved for voice phone conversations. (Hence they pass the low frequencies and are called "low-pass filters.") My first DSL service used a separate phone line from my telephone, so I was a bit leery of using these at first, but after using them, I can say they didn't seem to adversely affect the quality of either the voice or DSL service.
There is a maximum of the number of filters you can install per household. For example, the limit on the ones I have is five total. That may sound like a lot, but don't forget you will need these for every phone in your house as well as devices like your Tivo (DVR) or other satellite TV DVR, fax machine, caller ID unit, answering machine, & computer modem (assuming you still need to dial in occasionally). You can daisy chained several phone devices off of one filter with no problem. That is, if you have a fax machine with both line in and phone out jacks, plus a caller ID with both line in and phone out jacks and finally a phone, they can be hooked together and into a single DSL filter without a problem. Take care to get and install two-line models of these filters if you have two incoming lines in your home (e.g., you have a separate line for your home and home office or separate lines for your telephone and your fax machine).
Other than the physical input being telephone wire or coaxial cable, the cable and DSL modems can be treated more or less the same. (With FiOS, the ONT provides a standard Ethernet connection.) So the first step (if your ISP does not do this for you or if you are "self-installing" your modem) is to connect the coax or cable to your modem. For a DSL modem, the phone line clicks into the phone jack on the back of the DSL modem. (Don't confuse the telephone jack with the Ethernet port. For former is smaller than the latter.) The coaxial cable screws onto the cable connection on the back of the cable modem. Once you have done this, the rest of the installation is the same for either type of modem. (It is also the same from the point forward for FiOS.)
Next, you need to connect the Ethernet port on the modem to the WAN or Internet port on the router. The connection between the router and the modem may be one of those cases where a crossover cable (see the section on Cables) is necessary. The install kit will likely include a (very short) Ethernet cable, but it will not be a crossover cable in most cases. Some routers use MDIX (or auto-switching) ports on the WAN/Internet port, so a crossover may not be necessary. My approach is to try the cable supplied (assuming it is long enough to reach with your installation) and see if you get a link light. If you get one, great; if not, it's crossover cable time.
The figures below show an example of both a cable and DSL modem. We don't show a lot of choices here because there are many of them and generally your cable or DSL ISP chooses what modem you will be using. The ones shown here are reasonably representative of what is found in the wild.
The Motorola SURFboard SB5100 is representative of cable DSL modems. The lights on the front show (from top to bottom), power, (cable) receive, (cable) send, online, PC/activity, and standby.
The back of the Motorola SURFboard SB5100 has (from top to bottom) a 10/100 Mbps auto-sensing Ethernet port, a USB port, a terminal for the incoming coaxial cable, and at the very bottom a jack for the DC power supply input. Some cable (and DSL) modems will allow you to connect PCs (or a router and a PC) to both the Ethernet and USB ports simultaneously (respectively) assuming your ISP will allow you to have two IP addresses. Generally, you would only use one or the other and we emphasize the use of the Ethernet port in this tome.
The Westell WireSpeed 2100 is typical of DSL modems. From left to right, the lights indicate USB traffic, Ethernet traffic, (DSL line) ready, and power.
The back of the Westell WireSpeed 2100 has (from left to right) an incoming telephone wire jack, a USB port (rarely, if ever, used), the input jack for the DC power supply, a reset button and the Ethernet port. Like the cable modem, either the USB or Ethernet port, but not both is generally used. (And we again emphasize the use of the Ethernet port herein.)