Espaliered trees are great for producing fruit in a limited space. The main difference in care from a standard tree is the pruning.  While young, espaliered trees need to be trimmed at least twice a year.  They also require support.  This article  from Portland Nursery has a good explanation of care for these interesting trees, Espaliered Fruit Trees  http://portlandnursery.com/plants/fruits/espaliered-fruit.shtml. 

Pruning espaliered trees is a learned skill.  A good reference is the American Horticultural Society's Pruning and Training by Christopher Brickell and David Joyce, including a section of espaliered apple trees.  This article from OSU will give you basic information on pruning.  Training and Pruning your Home Orchard  https://catalog.extension.oregonstate.edu/sites/catalog/files/project/pdf/pnw400.pdf .   The Home Orchard Society  http://www.homeorchardsociety.org/ in Molalla gives courses on pruning.  Click on their calendar's highlighted dates to see offered courses. If you have several trees, it might be very helpful to have a professional pruner work with your trees and learn from them.   

Espaliered apple trees need the same care and feeding as standard apple trees.  This article from OSU has good information on Growing Tree Fruits and Nuts in the Home Orchard  https://catalog.extension.oregonstate.edu/sites/catalog/files/project/pdf/ec819.pdf.  Basically, when your trees are young, they are developing a root system and establishing themselves in your garden.  During this time pay close attention to watering needs, especially when we get very hot, dry weather.  Your trees will pull alot of water up from the soil, which  dries the soil faster that you would think.  Mulching with 3" of organic material around the tree (but not close to the trunk) will help limit soil moisture evaporation, moderate temperature changes in the environment and help control the weeds and grasses that compete with your trees for moisture. 

Fruit trees benefit from fertilization in the spring.  To determine what nutrients your soil lacks and your trees need is to have a soil analysis done.  It will tell you about the structure of your soil, and the levels of nutrients it contains and give you advice on correcting any deficiencies. That way you add the exact nutrients you need.   A&L Labs  http://www.al-labs-west.com/fee-schedule.php?section=Soil%20Analysis has an office in Portland and reasonable prices.