I don't like to be a implement of support you should do your own research on it, but this is what I know.
Mitosis is the conservation of ploidy as stated by Amitash and it has 6 phases. There is way more detail, but I don't think its all worth typing for a forum.
Prophase - the phase where the chromosomes condense, nuclear envelope starts to desolve, and the centromere move to opposite poles.
Prometaphase - the phase where nuclear envelope desolves and the mitotic spindles form (attaching microtubules to the kinetochores, position microtubules in the polar regions, and position microtubules in astral reagions).
Metaphase- The sister chromatids line up in the center of the cell and get ready for anaphase (should be 46 sister chomatids (chromosomes) lined up)
Anaphase - centromere divide on the sister chromatids and the sister chromatids are then seperated
Telophase - Nuclear envelope reforms, spindle dissolves, and chromosomes uncoil
Cytokinesis - the cell membrane segregates and the nuclei separate into daughter cells
Meiosis is the halfing of ploidy again stated beautifully by Amitash and is a 2 stage, 12 phase, and has a 5 step process
Prophase I - the phase where the chromosomes condense, nuclear envelope starts to desolve, cross-over occurs, and the centromere move to opposite poles. (summary)
Leptotene - the chromosomes thicken but chromatids are invisible centrosomes move to opposite poles
Zygotene - Homologous chromosomes pair (IMPORTANT POINT) and synaptonemal complex forms
Pachytene - synaptonemal complex is complete and cross-over takes place (IMPORTANT POINT)
Dipotene - Synaptonemal complex starts to disolve and depending on the organism the cell may arrest for later use (reproductive or germ cells)
Diakinesis - the nuclear membrane begins to disolve and spindles form
Prometaphase - the phase where nuclear envelope desolves and the mitotic spindles form (attaching microtubules to the kinetochores, position microtubules in the polar regions, and position microtubules in astral reagions).
Metaphase I - The sister chromatids line up in the center of the cell and get ready for anaphase (should be 23 homologous chromosome pairs lined up)
Anaphase I - centromere on the sister chromatids does not divide and the homologues are then seperated
Telophase I - Nuclear envelope reforms, spindle dissolves, and chromosomes do not uncoil
Cytokinesis I - the cell membrane segregates and the nuclei separate into genetically different daughter cells
Prophase II- the phase where the chromosomes condense, nuclear envelope starts to desolve, and the centromere move to opposite poles.
Prometaphase II- the phase where nuclear envelope desolves and the mitotic spindles form (attaching microtubules to the kinetochores, position microtubules in the polar regions, and position microtubules in astral reagions).
Metaphase II- The sister chromatids line up in the center of the cell and get ready for anaphase (should be 23 sister chomatids (chromosomes) lined up)
Anaphase II - centromere divide on the sister chromatids and the sister chromatids are then seperated
Telophase II - Nuclear envelope reforms, spindle dissolves, and chromosomes uncoil
Cytokinesis II - the cell membrane segregates and the nuclei separate into daughter cells
That should be some of the basics. I might be off son somethings so look it up. From Genes to Genome is a good book to start.