What is the process of fertilization in seed plants?
There are two groups of seeded plants, the gymnosperms and the angiosperms. Gymnosperms produce "naked" seeds and include the pines. Angiosperms are the flowering plants. I will explain the process of fertilization in the angiosperms.
The life cycle begins with the zygote or fertilized egg. The cells of the zygote divide by mitosis to produce the embryo. The embryo (and the zygote from which it originated) are located within the seed. When conditions are appropriate, the seed germinates to produce the sporophyte plant. The flowers of the sporophyte plant may produce both an ovary (female) and anthers (male). The ovary contains ovules. Each ovule contains a diploid megaspore mother cell with divides by meiosis to produce haploid megaspores. These megaspores divide by mitosis (3 times) to produce the egg and polar nuclei.
Within the the anthers there are initially microspore mothercells (diploid) which divide by meiosis to form the microspores which become the pollen grains (male gametophytes). These pollen grains can be dispersed by wind, insects, animals, etc. and eventually land on the stigma of another flower (typically on another plant). The pollen germinates to produce a pollen tube which grows down the style within the flower and leads to an ovule. The pollen divides to form 2 sperm nuclei which make their way down to the ovule through the pollen tube. One of the sperm nuclei fuses with the egg to form a new zygote and the other fertilizes the 2 polar nuclei to form the endosperm (provides nutrition for the embryo later on). This process is known as double fertilization and is unique to angiosperms.