How were other countries pulled into the conflict between serbia and aust- hungar?

Other countries were pulled into what would become the first world war thanks to numerous alliances and treaties. I will do my best to explain it below.

Austria-Hungary (AH) wanted to go to war with Serbia.

Russian did not want this to happen and intended to protect their interests in Serbia.

AH asked Germany to help fight on their side if it came to war, Germany accepted thinking it would not.

AH Sent Serbia a list of 10 demands they could never meet and said that if they didn't meet the demands they would invade, however Serbia replied saying it could meet all demands except for the 6th. AH invaded anyway.
Germany Declared war on Serbia because they had said they would, but they really didn't want to.

Russian Declared mobilized against Germany and AH but assures their friend Germany that they're only mobilizing against AH.

Germany devises the Schlieffen Plan to crush Russia's ally France very quickly and so that it could focus on Russia since Russia should have been slow to mobilize, however it became clear the France had no intentions of joining the war and Russia was mobilizing quicker than intended, so Germany claimed France bombed them and went to war with them anyway.

To circumvent France's heavily fortified boarders, Germany invaded Belgium and planned to use that as a passage way to France. Germany decimated both Belgium and Northern France, however the British Empire was upset that Germany invaded their ally Belgium and as such declared war on Germany.

British Colonies (Canada, Australia, New Zealand, India) were dragged into the fight thanks to technically being British.

Germany signs a secret deal with the Ottoman's to bring them into the Central Powers one day after declaring war on Russia.

Germany Declares war on Russia and so do the Ottomans.

Bulgaria, still upset because it lost a war to Serbia in 1913 joins the Central Powers.

Italy, although technically allied with Germany and Austria, decides to declare war on them because it never really liked Germany much anyway.

Japan sees this as an opportunity to take many of the German colonies in Asia, and so declares war on the Central Powers.

The USA remains neutral for most of the war, but towards the end (1917) enters as and independent power that fights alongside the Alliance.

The Russian Revolution (also 1917) begins and so they are forced to withdraw from the war.

Thanks to the British Colonies and America's intervention towards the end, the war swings in the Alliance's favour, Germany, Austria, Bulgaria, and The Ottoman's are defeated. America insists every world power dissolve it's empire, and they comply. Germany has many sanctions placed on them during the treaty of Versailles, everybody pretty much just blames them for the whole thing when it was really Austria's fault, this sets the stage for WW2.

And this right here is a very condensed version of the political scene during WW1

Do you mean israel ?