Before meiosis commences, chromosomes undergo replication. At the end of this process, each chromosome consists of a pair of sister chromatids that are joined together at the centromere.
Meiosis consists of two consecutive cell divisions; meiosis 1 and meiosis 2. It eventually results in the formation of four haploid daughter cells.
Prophase 1- Chromosomes begin condensing and homologous chromosomes each of which consists of two identical sister chromatids pair up. At different points along their lenght, chromatids of the homologues are crisscrossed. These points are known as chiasmata. The chromosomes trade segments at these points.
Centrosomes begin moving to the opposite poles of the cell with spindle microtubules forming between them. Nuclear envelope and nucleoli begin breaking up.
The spindle microtubules capture the kinetochores on the chromosome which then begin moving to the metaphase plate.
Metaphase 1- The chromosomes now lie on the metaphase plate. Microtubules from one pole of the cell are attached to one chromosome whilst its homologue has microtubules from the other pole attached to it.
Anaphase 1- The homologues, with the sister chromatids still attached together begin moving towards opposite poles of the cell.
Telophase 1- The homologues continue moving apart till they reach the opposite poles of the cell. Thus, each pole now has a haploid set of chromosomes, with each chromosome consisting of two sister chromatids. Cytokinesis may then occur, forming two daughter cells.
Meiosis 2 then commences.
Prophase 2- A spindle apparatus begins forming and the chromosomes move towards the metaphase plate.
Metaphase 2- The chromosomes lie on the metaphase plate with the kinetochore of each sister chromatid pointing towards opposite poles of the cell.
Anaphase 2- The centromeres of the sister chromatids seperate and the chromatids, which are now considered individual chromosomes, begin moving towards opposite poles of the cell.
Telephase 2- Nuclei and subsequently, nuclear envelope begin forming up at the poles of the cell. Cytokinesis then occurs.
The end result is four daughter cells, each with a haploid number of chromosomes.
Ultimately, your understanding of this process will be enhanced if you look at pictorial representations. So, do try to find such websites. Here is one site that has an animation on this process.