The first three words in Rex's effect explain it all. Your standard game plan should focus on summoning Rexterm and defending it.
It goes without saying, but our starting play is:
Only Domain: Activate Domain, use Therizia and Diplos as materials, Fusion Summon Kentregina. Then Kentregina effect, banishing domain to Fusion Summon Rexterm with her and a Dinomorphia.
Only Frenzy: Activate Frenzy, use Therizia and Stealthbergia as materials, Fusion Summon Kentregina. Then Kentregina effect, banishing Frenzy to Fusion Summon Rexterm with Stealthbergia and Diplos.
With both Domain and Frenzy, you can summon two Rexterms (Domain summon Regina, Frenzy summon Rex, then Regina copy Frenzy summon Rex). It can be useful when your opponent can only out one in a turn. However, against opponents that use board breakers like Raigeki or Super Poly that can out multiple in one go, it is often wise to use only one Starter first to go into Rexterm. That way, you can just flip the other starters when your first Rex gets outed.
Your opponent will do anything at their disposal to answer Rex, and it is weak against staples such as Raigeki, Talents, or Imperms, so make sure to use your negates and removal wisely. Matchup knowledge is pretty crucial to determine which moves could potentially out Rex and should be stopped. For instance, if you are against Tearlaments and see the opponent trying to summon a lot of monsters, that telegraphs us that they are going to out Rex with Underworld Goddess, so it might be best to use your set Ferret Flame just before that could happen. However, some decks such as Branded are unlikely to run Underworld Goddess, so you can hold the Ferret Flame for better timing.
For most matchups, defending Rexterm clearly should be a priority. But what about other monsters?
Thanks to our monsters' floating effects, we are somewhat resilient to destruction, and in fact, it may be able to accelerate our game plan, as Therizia (and to a lesser extent, Diplos) generates resources when they are summoned. Judge wisely whether you should let the opponent destroy your monster or not, as it can change the course of the battle.
Sometimes the opponent can do a favor for you. In the above scenario, I would not be able to prevent the opponent's Branded Banishment if Albaz does not attack Diplos.
Some decks just don't care about Rexterm, such as those that mainly focus on the back row. In that case, aiming to control the opponent with Kentregina's copy effect might be better.
If you are going first and see your opponent only setting backrow and not summoning any monster, then there is a high chance that they are using trap decks, which of course, do not really care about Rex's effect. In that case, you have to destroy those backrows before they become live.
In such situations, Kentregina and Brute will really shine.
Sample scenario:
You went first, having Therizia, along with Domain and Brute set. Now is the opponent's turn, and they used Prosperity revealing their deck to be a backrow deck that is low on monster. They set five and are about to end their Main Phase.
In that situation, you know that Rex won't do much against them, and it will be better if you clear as many of those backrows as possible before the turn passes, as well as set up a follow-up negate for the next turn.
Activate Domain, summoning Kentregina;
Activate Brute, destroying Therizia and one backrow;
Therizia floats into Diplos, banishing any trap except Brute;
Activate Diplos, sending any trap;
Activate Kentregina copying Brute, destroying Diplos and one more backrow;
Diplos floats into Therizia, banishing any trap;
Activate Therizia, setting Sonic (or second Brute).
That way, you have cleared two backrow and have one negate (Sonic) ready for your next turn.
An example of controlling with Kentregina and Brute
If you are going second, have no starter but Diplos and Imperm in your hand, and your opponent controls an attack position monster, you can activate Imperm on the opponent's monster, summoning Diplos that dumps Therizia, then crashing Diplos to the opponent's monster. That way, Diplos' floating effect will summon Therizia (by banishing Imperm as a cost).
Crashing your Therizia/Diplos to an opponent's Defense Position monster is also a viable way to quickly reduce your LP during the early game when going second.
Holding your starters until the opponent has made some moves might be a good idea, as you don't want them to outright Imperm or Gamma your Kentregina, nor having them chain Shifter to your starters. Even letting your opponent attack you (non-lethally) and starting your play at the end of MP2 after your opponent has set all of their Spell/Trap is sometimes a good strategy, as it lowers your LP and turns off their Quick-Play spell (because they set them).
Rex's ATK suppression effect can be used in the damage step, and it is preferred to do so. That way, the opponent will not be able to chain cards that otherwise will result in Rexterm's demise (such as Impermanence or Ghost Ogre).
If you have both Domain and Frenzy set, you may want to flip Domain first to bait an opponent's Ash, as it is more lavish than Frenzy.
If you only have Domain and Diplos in your starting hand, you can summon Diplos to dump Frenzy so your Kentregina can copy it instead of Domain on the next turn.
If you have Rexterm and Ferret, you can Chain Link 1 Rexterm, then Chain Link 2 Ferret to make Ferret more destructive. Keep in mind that you have to make sure the opponent does not have any play that will require you to use Rex's effect again, as it is once per turn.
Paying half your LP when your LP is odd will cause the resulting LP to be rounded up (i.e. when your LP is 125, you will technically pay 62.5, leaving your LP to 62.5, then it will be rounded to 63). This also means that you can always pay half, even at 1 LP, with a practically free cost!
Note that in Intact's case, the one that will be rounded up is the damage you take. So, even under its effect, taking battle damage while at 1 LP can actually be lethal.
We are a control deck. This means that we need to understand the opponent's deck more than our own. Springing your interaction in the right moment to isolate their plays is key to victories. This applies not only to this deck but also to other control decks. Refer to the "Enemies" section for more detailed tips against some matchups.
Keep track of the cards in your opponent's hand. That way, you can better predict the opponent's move and how they can answer your board.