How do I get the thing to cut the small trees that say they need to be..

You need to teach one of your Pokemon HM01 (Cut) to cut down little trees. HM01 (Cut) can be obtained from the man in the Ilex Forest after you are finished with chasing the Bird Pokemon.

Hope this helps!

First of all you need to do is go to the house in the left and it would say kurt's house meet him and help him save slowpoke in the well and go in the left path your rival will challenge you defeat him then got to the alex forest and meet the guy near the tree which says you need cut and talk to him and he says you find a Pokemon find it and return the other guy he will give you cut