Arduino with Android and iOS

Hi, how it connects Arduino with Android and iOS? any suggestions for the first connection, thank you.

What do you mean by connect?
If you want to exchange data from one to the other, you could use bluetooth or wifi.

Arduino controlled by phone with bluetooth module with both iOS and Android

I tried to use that platform xamarine work and gives me the following error after you install the package:

Could not install package 'Microsoft.IoT.SDKFromArduino 1.1.1'. You are trying to install this package into a project That targets 'MonoAndroid, Version = v7.0', but the package Does not contain any assembly references or content files are compatible with That That framework. For more information, contact the package author.

Don't know about that specific package, i've never used it.
The only thing You need to do is write a program for android and/or ios that sends some command which You define. Arduino has to interprete the data/command as soon as it receives it and perform the desired task. You can use SerialEvent.
I've done this with multiple ic's connected to the same serial "bus" and with wifi connection. All You need to do is to define a communication protocol.

I can give some examples? and because the first time I do it.
NuGet which package you use for programming with Arduino? and how you make a first connection with bluetooth?

here you have a video with program code on how to communicate with arduino over bluetooth: