I'm not quite sure how the deck properly works but here we go folks. Please note this is a work in progress with the Primer, so if you have suggestions, let me know so I can try to improve it. This is just based on my experience and I'm not the greatest pilot to this deck so this is just based on my understanding.
1. Main Combo Line:
Two Card Combo:
Ritual Beast Tamer Elder and Spiritual Beast Cannahawk are your two card combo — for the most part you will be using these two to pop out and show'em what Ritual Beasts (RB) is all about. Normal Summon Elder for the added normal summon. Passive effect of Elder allows for an additional normal summon for any Ritual Beast card. Please note: Spiritual Beast cards count as Ritual Beast cards because it states spiRITUAL BEAST and there are valid cards for the normal summon.
Effect of Cannahawk allows you to banish one 'Ritual Beast' card from deck. Here you will be grabbing Spiritual Beast Tamer Lara.
Lara is your bread and butter for the most part. You do NOT activate Lara's special summon effect when she is banished yet. With Elder and Cannahawk safely on field, contact fusion the two cards to special summon Ritual Beast Ulti-Cannahawk. To RB contact fusion, you banish one Tamer and Beast from field and special summon a fusion RB monster (note this does not count as a fusion summon, but is affected by the fusion cards such as Defusion)
With Ulti-Cannahawk in play and three ritual beast cards, activate this card to send two cards from the banished zone to the GY, and chain the effect to the secondary effect of sending Ulti-Cannahawk back to the Extra Deck. The ruling with Ulti-Cannahawk works by allowing you to special summon back one of your Ritual Beast Tamer and Spiritual Beast from banished zone to field, and then as long as you have one target to send back to the GY, the search effect will go through. You're gonna search Ritual Beast Inheritance with Ulti-Cannahawk's effect.
With Ritual Beast Inheritance, you will need to grab either (mainly) Ritual Beast Tamer Wen or (rarely) Ritual Beast Tamer Lara for the next play. On field, DO NOT FORGET TO ACTIVATE CANNAHAWK'S EFFECT. Because Spiritual Beast Cannahawk is a soft once per turn, as long as it leaves the field and comes back, you can keep on activating the effect when you recycle the card back to field. You will ideally send off Spiritual Beast Rampengu the banished zone with this effect for the first time, and any repeating time it's any Spiritual or Tamer cards based on what you need. With the Ritual Beast Tamer Elder and Spiritual Beast Cannahawk on your field, you can link off into Ritual Beast Ulti-Kimunfalcos.
With this ability, you can banish one ritual beast card from your GY (the one you sent using Ulti-Cannahawk) and then perform a normal summon after it resolves. At this point you can bounce back Ritual Beast Ulti-Kimunfalcos if you need to dodge any negates. You'll normal summon Ritual Beast Tamer Wen and grab for this play. You'll special summon Spiritual Beast Rampengu from your banished zone and activate his effect to banish one extra deck 'Ritual Beast' monster. The play here is to send a psychic type monster, ideally your copy of Ritual Beast Ulti-Gaiapelio as this is less integral to your plays. With that, you will send Spiritual Beast Tamer Winda to your GY. With both Winda and Lara in your GY, you'll banish them from the GY to contact fusion Ritual Beast Ulti-Nochiudrago and from there you'll need to activate Spiritual Beast Tamer Lara to special summon from the main deck. At this point, the line varies depending on what you're facing. I'll include the main two variations I know.
2. Archnemese Line:
With two level 4 monsters on the field, you'll need to xyz summon into Infernal Flame Banshee.
From there, you activate the effect to detach a material and search for one Pyro monster and add it to your hand. Here, you will search for Nemeses Flag and activate its effect.
Here is where deviation occurs. If you're more into your protos lines, you'll idealistically grab Archnemeses Protos to your hand, and you'll banish three cards of different attributes, one being Infernal Flame Banshee as cost. Alternatively, if you don't have Protos (which I don't), you can use Archnemeses Eschatos as another target - as it is cheaper to buy. The main difference is Archnemeses Eschatos is not as great as it only uses types and not attributes and with limited attributes in the current meta (as of writing), it has a limited effectivity on field. If you can buy a Protos, please do.
Now with Banshee banished, and Protos on the field, you will special summon out Banshee as you will still have Nemeses Flag on the field. With Protos on field, you should have the attribute you need to prevent from summon - Fire, Light, Dark or Wind. Up to you really what you need. As of wrting this, the main matchup is Fiendsmith Snake-Eyes, Yubel or Tenpai, so this is really an optimal line.
3. Colossus Line:
With Colossus, you'll need to follow the plays up until you search for Protos, in which case, you'll search for Nemeses Corridor instead of Protos.
Because Thunder Dragon Colossus can be summoned using it's secondary condition, you will special summon it after Nemeses Corridor is summoned by tributing Corridor. That's the alternative line for the Flag play.
4. Alternative Line 1:
by the chance you don't get to go into the lines, there are some alternative plays you can use based on the extra deck I have here. The lines are a bit more complex based on the hand and field you get given.