Fun facts about apples ...

The short answer is "Yes", and it's not difficult.  Firstly get some nice ripened pips from an apple that you like (ripe pips often 'rattle' inside the apple when you shake it).  Eat the apple, take out the pips and plant them in a pot of moistened compost.  Put the pot away somewhere outside, remember to water it occasionally to prevent it from drying out too much, and be patient!  The pips may take more than a year to germinate, and almost always benefit from a cold winter spell (or a week in the freezer!).   If a seedling grows, then be patient again - for it is unlikely to flower and fruit before it is 3 or 4 years old.  That's about it.   You can of course train the young tree into a fancy shape to grow against your wall, or let it be more free-form planted in your veg patch, or at the back of your border.  In due course - you will be able to harvest your own unique fruit.  For (and this is the important bit)  because it has been grown from a pip, and apples DO NOT come 'true to type' from a pip - then your new apple tree will be a 'one-off' and as such, you can even name it whatever you like!  Beware, however - that many millions of apple seedlings have been raised by professionals and amateurs alike - with a vast amount of them being truly awful, and only a very few having gone on to greatness!