Stereo recording is capturing two independent signals and storing each in a single track - one left, one right. For stereo recording you need either <1> a single microphone that uses two diaphragms inside a single enclosure, usually referred to as a single point stereo mic, or <2> a pair of (mono) microphones each with a single diaphragm. Examples of single point stereo mics: Rode NT4, Audio Technica 822, Studio Projects LSD2, AKG 422 / 426, AKG C34. Most other mics used here are pairs of single mics. Doubling up the signal from a signal mic so the same signal is on both the left and right is just dual mono, not stereo.
Most of the recorders used by people here are 2-ch or 4-ch recorders. They all record stereo, or even two stereo pairs. The H4 will record in stereo, as will the M-Audio MicroTrack, Edirol R09 and R-4 (4 channels), Marantz PMD-671 and -660, Tascam HD-P2, Sound Devices 722 and 744 (4 channels), etc.
Most recorders with XLR, RCA, or 1/4" inputs are set up so that each input connector records a single channel - only left, or only right. Recorders with mini-connectors (like the mic-in on the MicroTrack, the R09, iRiver Hx00, JB3, etc.) record a stereo signal - both left and right channels - via the single connector.
In order to get a stereo recording with the H4, you need to send it a stereo signal, i.e. an independent left channel and an independent right channel. One may do so either by using two (mono) mics as noted above, or by using a single point stereo mic that has two outputs. Some single point stereo mics output over a pair of XLR or 1/4" connectors, and some output over a single stereo-mini connector. If the latter, then you'll need adapters to convert the stereo-mini connector to a pair of XLR connectors for inputting to the H4 (or a pair of mono 1/4" connectors if the H4 uses dual XLR-1/4" connectors).
We really need to know the mic in use in order to provide more specific info about how (or whether or not it's possible) to capture a stereo recording with the gear in question.