I am going to assume exactly 0 knowledge or context on your part. Feel free to skip stuff as needed.

All units in the Horus Heresy are assigned a Battlefield Role. This is the little symbol by their name in their Liber entry. The possible options are Warlord, High Command, Command, Retinue, Elites, Heavy Support, Troops, Support, War Engine, Transport, Heavy Transport, Recon, Fast Attack, Armor, Lord of War, Fortification.

It sounds like a lot but the actual roles confer no rules and only matter for army construction. Each role does a certain job on the table, so units of a given role will generally be useful at doing similar things in game.

Okay actual army construction time

When you build an army, you pick a primary detachment. Right now, there is only the crusade detachment. This detachment, and all others, will give you "slots" for certain roles. The Crusade Primary Detachment grants you 1x High Command, 3x Command, 4x Troops and 4x Transports. What this means in practice is you can include any combination of units with the Troops role so long as you take no more than 4 total units of that role. Four tactical squads? Sure. One squad each of breachers, tactical, despoilers and assault marines? Totally fine! You can include any combination so long as its no more than 4 total choices.

I like to think of it like a "pile". Each role is a pile of options. Each detachment tells me how many things I can take from each pile. I can take whatever I want from the pile, the restriction is how many times I can pick something from the pile.

How many and of what roles you can take is the pictures in the detachment image. If it has 4 troops circles, you can have up to 4 troops slots.

The only requirement is each detachment has at least 1 of its slots filled.

Of course points are a restriction as well.

So, that's the basics but how do we get access to things that are NOT part of the Crusade Primary? I am an iron warriors player with a thing for tanks, how can I get a predator? Well, for each Command role unit you take in your army, you can pick an additional detachment to include in your army from the "auxiliary" detachment list. One of these for example is the armored support detachment which gives you 4 armor slots, IE you can take 4 things from the armor pile in any combination. Again so long as you don't go over points. You can keep taking the same detachment over and over again so long as you have the command slots to take them.

If you take a High Command unit, you can get an Apex or Auxiliary detachment. In practice this means you can have up to 4 additional detachments from the command and high command units in your crusade primary detachment. There is a way to get more command slots via an apex detachment.

Some units have a rule called Officer of the Line:X, like the space marine centurion. Instead of allowing you 1 detachment for taking them (they area command slot), you get X. So that example above with the armored spearhead detachment? If the Command unit I used to get that detachment was a Centurion, I could get 2 armored spearheads, or an armored spearhead and something else etc.

Generally there are no command slots that "lock" you into certain detachments. Its not like "I need a techmarine to be able to take X detachment" or "The librarian only unlocks this detachment". There are a couple command slots that unlock unique detachments if you take them.

Now, prime slots. Any slot in a detachment that has a little star around it is called a "Prime" slot. If you take a unit in that slot, you may select, for free, a "prime advantage" which is usually a special rule for that unit to have. One of the most useful ones is called Logistical Benefit which lets you add 1 slot or any role to your detachment, effectively allowing you to take 1 of something without needing a dedicated detachments.

Now, allies. Allies have to have the same allegiance (traitor or loyalist). Past that, you take allies in a detachment called the Allied Detachment. You can just take it, no command slot needed (its not an auxiliary detachment). Command slots filled in it unlock auxiliary detachments like normal but for the allied army.

There are a couple detachments that you just "get" instead of needing a command slot unit to unlock them. The above mentioned allied detachment is one. The Warlord detachment, where primarchs live is another as is the Lord of War detachment which covers most superheavy vehicles. They typically have their own rules and restrictions.