Communications: We have a VHF (short distance) radio on board, as well as an ICOM M-710 SSB (Single Side Band) long distance high frequency radio. We mostly use the VHF for talking to other cruisers, tuning in to the various "cruiser nets" we come across, and hailing other ships, marinas, or services who monitor their VHF. We use the SSB radio to listen to cruiser nets and picking up weatherfax broadcasts. We have the means to send/receive emails through our SSB too, but use our satellite phone instead.
We use our Iridium satellite phone for email and for receiving weather forecasts. Our service provider, UUplus, has been great so far allowing us to use the data phone connection for about a buck a minute. FYI, we can usually send and receive all emails (text message only) each day we use it, including weather information requested, in a minute, sometimes two, anywhere in the world. In addition if we ever need to place or receive a call, especially emergencies, we have the option.
Instruments: Dreamkeeper has a Raytheon SL70 chartplotter in the navigation station, plus a repeater at the helm. This allows us to view with one screen all the data being processed by all our instruments: speed, gps, depth, wind, radar, etc. We also use our plotter for navigating by inserting "navigation cards" for the areas we travel to. For example, we have been using one card that has all the chart info on it for all of California and Mexico. It has been amazingly accurate except for the area in and around Banderas Bay, Puerto Vallarta, where it shows us on land by a couple of miles.
We also have a seperate instrument for wind and another "multi-instrument" that measures most everything linked together with the Sea-talk system by Raymarine.
When motoring we often use the electronic autopilot that is also connected electronically with all the above instruments.

Navigation: We carry paper charts for all the areas we will be traveling. As stated already, we also use our "plotter" to view electronic charts right at the helm, which really makes things easier and much safer, especially at night coming into new places. For example, we can "split the view" of the plotter screen to show a navigational chart in detail on one side, and have the radar screen up on the other side simultaneously looking at our route and potential obstacles. This, of course, does not take the place of our eyes and our senses which we believe are always more important then any electronic gadget out there!
When we plan our passages we often look at both the paper charts and the electronic charts to plot our course. Then we come up with "waypoints" that lay a course for our intended route. We input the waypoints into the plotter and double check them on paper to make sure they are correct. This way everything is redundant and allows us to have good piece of mind in case our electronics were to go out by a lightening strike or "Uncle Sam" turning off the GPS system while we're in the middle of the ocean.
While underway we keep a "running log" in our logbook with info like gps coordinates, wind, barometer reading, speed, etc. We try to do this about every hour or so, most importantly at night, as one of us is sleeping and a running record of the journey could be super important. It's also important so we can track the weather with wind info and barometer readings over time to monitor for pressure increases or sudden drops.
If all else fails, we can use our Astra III-B sextant. I took an 8-week course in celestial navigation and passed the U.S. Sailing certification test in the art. However, it's a skill you need to practice and use, so one of my goals through the south pacific is to take sun and star sights often, keeping the skills sharp. I'm also going to try to teach Nicole the best i can. Knowing how much she loves math, it will certainly be a lesson in patience. :)