Both pteridophyte and bryophyte show haplo-diplontic life cycle. While the diploid phase is not independent in bryophytes, it is independent in pteridophytes. Moreover, the  sporophyte is more conspicuous in pteridophytes than in bryophytes. Sporophyte is the dominant phase in life cycle of pteridophyte.
The given figure shows the haplo-diplontic life cycle. 

Sporophyte: The sporophyte is well developed plant body.
It is differentiated into true roots, stem and leaves. Vascular tissue is well developed in these parts of the plant. The sporophyte bears the sporangia. Sporangia are subtended by leaf-like appendages called sporophylls. 

Formation of Spores: The spore mother cells in the sporangia undergo reduction division to produce spores.

Germination of Spores: Spores germinate to produce the gametophyte.

Gametophyte: Gametophyte is small but multicellular. It is free-living and usually photosynthetic. It is called prothallus. It bears antheridia and archegonia which produce male and female gametes. Transfer of male gamete takes place through pollen tube and then fertilization takes place.