One of the major unresolved issues regarding magnetic reconnection at the dayside magnetopause is the location where reconnection first occurs during periods of a large interplanetary magnetic field By. In order to address this issue, we examine and contrast the onset of reconnection in the presence and absence of a finite guide field (By). In an accompanying paper (Karimabadi et al., 2005) we showed that in case of one linearly unstable mode, tearing saturates at amplitudes too small to be of relevance to transport at the magnetopause, even in the antiparallel case. However, we show that in general a number of modes are simultaneously unstable at the magnetopause. This process is aided by the presence of electron temperature anisotropy which broadens the unstable spectrum, extending it to very short wavelengths. Multimode tearing gets past the single mode stabilization and grows to large amplitudes in several stages: the initial linear stage, the coalescence process which proceeds at a slower growth rate, the growth and dominance of the longest wavelength in the system, and a final explosive phase which leads to a saturated state with a bifurcated current sheet. The aspect ratio of the magnetic island at the end of the explosive phase is ~0.2. This is in good agreement with the aspect ratio of the magnetic island structure at Earth's magnetopause reconstructed from the single-spacecraft data by Hau and Sonnerup (1999). We find that in addition to coalescence, there can occur stretching of the X lines. This leads to a recurrent reconnection process where only a single, rather than a pair of magnetic structures are periodically produced, reminiscent of flux transfer events. Although the detailed properties of the various interacting modes are altered in the presence of a guide field, the basic scenario including the final explosive phase of the system remains even for very large guide fields. We calculate the steady state reconnection rate as a function of guide field and plasma beta and show that fast reconnection is obtained even for modest values of guide field. Detailed application of these results to the magnetopause is discussed. One key finding is that it takes a very weak guide field of less than 0.07 of the magnetosheath field to transition away from the antiparallel reconnection. The linear growth rate of isotropic tearing compared to convection time is fast only for thin sheets. In the absence of electron temperature anisotropies, both antiparallel and component merging remain competitive as long as the guide field is not too strong (≤0.4). Local condition, most importantly the shear flow, is identified as one effect that may change the behavior of reconnection in the antiparallelversus component merging.