How can you calculate the ELO ratings of a chess player?

When you play rated games you 'll have after some games an ELO rating,an ELO rating is based on the results you made against the players you have played. An example your results were 10 points (winning is 1 point,remise is 1/2 point)on 20 games and you have played to players with an average ELO of 1750 points,then you'll have an ELO rating of 1750 , when your results are above 10 points your rating is higher then 1750.,when your results are less your rating is lower then 1750. When you have 15 points in this example I think your rating is 1943 and by 16 points it 'll be 1990 ,but I'm not totaly sure of it. Your rating is based on the possibility what your results should be when you play against a player who has an ELO rating too and my rating (arround 1850 ELO)means when I play to players with the same ELO points the expected points are 50-50 ,when I play against players with 2090 ELO on 100 games I play to I have to make 20 points to hold my rating the same 1850,when I play against players with 1610 ELO ,I must have 80 points to hold 1850 ELO. When I'm above this expected points my rating goes up,when the results are lower my rating goes down.

As I remember from when I was in a chess club, you start off with an average score (can't remember what) then you adjust your score when you play games. Your score goes up when you beat a higher rated player and down if you're beaten by a lower rated player. The games need to be carried out under tournament conditions to really count. Sorry I couldn't be of more help but I hope that's of some use to you.

In general you'll just have to play rated games against other rated players to figure out a good estimate of where you stand. There's not really any other way (that's accurate).