Data Modes
These modes are a way to use amateur radio without the need for voice communication. A low power radio (QRP); less than 10 watts is all you need to be successful on digital modes. Here are a couple YouTube videos that explain the processes. An external sound card connected to your radio via a USB interface to your computer and WSJT-X is all you need.
FT8
In 2018 it is by far the most popular digital mode for award chasing and working DX. It is described in this news story. The WSJT-X software can be downloaded from Joe Taylor's website. Gary ZL2iFB has written an FT8 Operating Guide.
Packet
Packet - One of the first "modern" digital modes, packet radio transmits data in groups or "packets" of 10s or 100s of bytes. This allows improved throughput and error control. The basic protocol for packet radio is AX.25. Transmission speeds typically range from 300 bps on the HF bands to 1200 and 9600 bps on VHF or UHF.