To understand the concepts and language of international law, it's best to start with dictionaries, encyclopedias and specialized sources of international law used by practitioners and scholars. Let's start by finding a definition for International law. Using the e-book below, go to the contents section and select I. Scroll down to look for the definition of international law (when using a dictionary, it is sometimes easier to scroll to the right spot than to use the browser search to look for the term. However, if you do want to try using the browser search, be sure to put your search terms in quotation marks).
Dictionary of Public International Law by Next, let's figure out the difference between public and private international law. Using the below e-book, use the same process, go to the contents section and select I. Scroll down to look for the definition of international law (when using a dictionary, it is sometimes easier to scroll to the right spot than to use the browser search to look for the term. If you want to try using the browser search, be sure to put your search terms in quotation marks). To compare this with the definition for "private international law", repeat the process, looking in the P section.
Parry and Grant Encyclopaedic Dictionary of International Law by Scrolling through International Law Dictionaries online can be quite tedious, so if you are in the library, you may prefer to use some print dictionaries:
Modern Dictionary of International Legal Terms by 
Dictionary of International Trade by Another good source for understanding International law concepts is:
Note that this link takes you to multiple Max Planck Encyclopedias of International Law. In the search box at the top right, search for "international law". Before you examine the articles, take a moment to notice the filters on the left side of the page. If you open the section called Module, you will notice that there are two encyclopedia that you are searching through, Max Planck Encyclopedia of Public International Law [MPEPIL] and Max Planck Encyclopedia of International Procedural Law [MPEiPro].
Going back to your search results, the first article in your search results list provides you with a more comprehensive explanation of international law.
These definitions may seem a bit confusing, so for a more straightforward definition of international law that clearly explains the difference between public and private international law, you can review this entry from Wex, the legal dictionary and legal encyclopedia provided by the Legal Information Institute at the Cornell Law School.
Now that you understand the difference between those two concepts, let's examine a study aid as the fastest way to get up to speed in a general way.
Public International Law in a Nutshell by In Chapter One of the above study aid, you will find a modern definition of international law. Notice that they get their definition of international law from:
Students and scholars in the United States often use The Restatement of the Law: The Foreign Relations of the United States as a guide to identifying international law as applied in the US. The full definition of international law provided by, this text is:
"International law, as used in this Restatement, consists of rules and principles of general application dealing with the conduct of states and of international organizations and with their relations inter se, as well as with some of their relations with persons, whether natural or juridical."
To understand this definition in context, you need to go to Chapter 1. International Law: Character and Sources, § 101 provided below and review the comments.
The other relevant restatement on International law is:
Learning to do research on international law, requires you to understand what sources of law are considered relevant by international practitioners and scholars and what relative weight they give to these sources. Going back to Chapter 1. International Law: Character and Sources, of Restatement (Third) of Foreign Relations Law:
(1) A rule of international law is one that has been accepted as such by the international community of states
(a) in the form of customary law
(b) by international agreement; or
(c) by derivation from general principles common to the major legal systems of the world.
(2) Customary international law results from a general and consistent practice of states followed by them from a sense of legal obligation.
(3) International agreements create law for the states parties thereto and may lead to the creation of customary international law when such agreements are intended for adherence by states generally and are in fact widely accepted.
(4) General principles common to the major legal systems, even if not incorporated or reflected in customary law or international agreement, may be invoked as supplementary rules of international law where appropriate.
It's important to use the link above to go to the section and review the comments to fully understand what is meant by concepts like "practice of states" and what qualifies as evidence of this type of law. The comments also provide definitions for opinio juris and jus cogens. The Reporter's note references Article 38 of the ICJ Statute which is linked to further down on this page.
The next section of Chapter 1. International Law: Character and Sources, of Restatement (Third) of Foreign Relations Law, § 103, explains what is considered reliable evidence of different types of international law sources.
(1) Whether a rule has become international law is determined by evidence appropriate to the particular source from which that rule is alleged to derive (§ 102).
(2) In determining whether a rule has become international law, substantial weight is accorded to
(a) judgments and opinions of international judicial and arbitral tribunals;
(b) judgments and opinions of national judicial tribunals;
(c) the writings of scholars;
(d) pronouncements by states that undertake to state a rule of international law, when such pronouncements are not seriously challenged by other states.
To fully understand the meaning of this section you need to click through the link above and review the text as the Comments and the Reporter's notes.
For another reliable source of information on the sources of international law, consider this:
Article 38 of the "Statute" furnishes an indirect answer to the question: What are the texts of international law? The article is written in terms of what sources the court will use in order to resolve a dispute. These sources include treaties, customary law, case law, academic writings, and general principles of law. Article 38 reads:
Many of these definitions may yield more questions than answers. You may want to understand more deeply what is meant by and how to find evidence of different sources of international law.
Search in Wex for "international convention" and "customary international law".
Using:
Review the entries for:
A useful, brief introductory source on international law that defines many of these concepts is:
To understand the possible hierarchy of the sources of international law. Review Chapter 29 Sources and the Hierarchy of International Law: The Place of Peremptory Norms and Article 103 of the UN Charter within the Sources of International Law, in
The Oxford Handbook of the Sources of International Law by 
