How states choose judges for trial courts and for apellate courts???

There are multiple ways but some more usual ones are Appointment in which the states governor or legislature  will choose the judges. The second is called merit selection in which the judges are chosen by a legislative committee based off of the judges past records. Here is a link that gives more of the ways and in more detail as well:

https://litigation.findlaw.com/legal-system/how-are-judges-selected.html

abraham lincoln  (february 12, 1809  – april 15, 1865) was an american statesman, politician, and lawyer who served as the 16th  president of the united states  from 1861 until  his assassination  in april 1865. lincoln led the nation through the  american civil war, its bloodiest war and its greatest moral, constitutional, and political crisis.[2][3]  he preserved the  union,  abolished slavery, strengthened the  federal government, and modernized  the u.s. economy.