New smartphone and SIM card - how to transfer data (e.g. Mobile phone numbers)?

I'm going to buy a new cell phone with a new contract soon. In other words, I'll get a new SIM card, but I'll keep my old phone number. How can I best copy all the data from my old smartphone, especially the cell phone numbers, to my new smartphone? But also pictures and such?
My old smartphone is a Huawei, my new one is a Samsung.

There are apps for this. You can also, for example, synchronize the addresses with the help of Google.