There are two important things here:
(1) Check if you need a visa in advance - the rules changed in July 2023, and most nationalities now need to obtain a visa
(2) Make sure your passport is stamped when you enter Paraguay
Whilst these two things might seem obvious to you, it's important to note that in some areas, the border with other countries is fully open (i.e. there is no passport control at the actual border), and in other cases, even at an airport, the immigration official checking your documents might not stamp your passport, if it is not technically needed at that time. Examples of this include if you are entering Paraguay using a passport which does not require a visa to enter Paraguay as a tourist, or if you are already a resident of another Mercosur country and can enter using your Cedula (ID card) rather than needing a passport at all.
Part of the process of obtaining residency in Paraguay is checking that you entered Paraguay legally - and this means proving it, beyond all doubt. The way to do this is to make sure your passport is stamped at the point of entry, by a Paraguayan immigration official.
Additionally, nationals of most countries now need to have obtained a visa to be able to get residency - note that this doesn't necessarily mean you need a visa to enter the country generally, but you may need to obtain a visa to be able to obtain residency.
Is a visa needed to enter Paraguay?
This depends on your nationality. There are three broad categories:
(a) Nationalities which do not need a visa to enter Paraguay, and can simply show their passport when they arrive, whether coming to get residency or just for a holiday etc
(b) Nationalities which do not need a visa to enter Paraguay generally, but do need one if they want to obtain residency, which can be easily obtained from a Paraguayan embassy in another country
(c) Nationalities which require special permission to enter Paraguay, from the Paraguayan Foreign Ministry
To check whether or not you need a visa to enter Paraguay, and what the relevant processes are, please refer to our full article on this topic: Nationalities that need a visa to enter Paraguay.
Summary
This step is very simple - just get a visa if you need one, enter Paraguay legally, and get a stamp in your passport to prove it. Congratulations! You're now in Paraguay, and can apply for residency here. Next up it's Step 3: Meet the Government.