If you refer to a single fiber strand you'll need an SFP module supporting "BiDi" fiber - 1000BASE-BX(10), 10GBASE-BR/"-BX" or similar. Single strands are also used for shared fiber architectures, most prominently GPON, where you require active termination of the fiber (an ONT).
While it is possible to optically multiplex a (perhaps more common) dual-strand Ethernet variant onto a single strand, requiring wavelength conversion, it usually isn't cost effective. In any case, if the other side is already terminated you'll need to match the SFP module to its physical-layer variant.
Optical connectors vary. The most common kinds:
LC duplex connector (used on SFP modules, high density, most common)
SC duplex connector (still common)

Pair of ST connectors (legacy)
For a more complete list, see Wikipedia.