This is a huge question and books and books have been written on it.
I'll give you a couple of the major impacts:
- It killed a huge proportion of them. Some estimates believe that European settlement killed 90% of all Native Americans either in warfare or (more importantly) via disease.
- It took away their independence and pushed them farther and farther west, eventually on to reservations much later in history.
- It changed the way many tribes lived even before whites got anywhere near them. For example, the Plains Indians' horse culture was not possible before the Europeans came. Europeans brought horses and technology that changed the way Indians lived their day to day lives.
- In the short run, it changed the balance of power among tribes. Tribes who allied with the whites became more powerful.
There are surely more impacts and more detailed discussions of the ones I've mentioned, but these are some basics.
Even more than the obvious effects on the people, the appearance of europeans forever altered the history of the First Americans. It is almost analogous to the possible effects of an alien race appearing on Earth. Everything they knew, had known and were still to discover altered irrecoverably.
Perhaps one of the most insidious effects was probably that most who died from the appearance of Europeans and the resultant epidemics they caused perished without ever seeing the cause. The conquistadors tell of areas called "desplobado" or simply uninhabited although it appears that they should have people living there.