The newly baptised are immediately annointed with holy oil and freed from sin

After this, when we have issued from the font, we are thoroughly anointed with a blessed unction,—(a practice derived) from the old discipline, wherein on entering the priesthood, men were wont to be anointed with oil from a horn, ever since Aaron was anointed by Moses. Whence Aaron is called “Christ,” from the “chrism,” which is “the unction;” which, when made spiritual, furnished an appropriate name to the Lord, because He was “anointed” with the Spirit by God the Father; as written in the Acts: “For truly they were gathered together in this city against Thy Holy Son whom Thou hast anointed.” Thus, too, in our case, the unction runs carnally, (i.e. on the body,) but profits spiritually; in the same way as the act of baptism itself too is carnal, in that we are plunged in water, but the effect spiritual, in that we are freed from sins.

Tertullian
On Baptism
Chapter VII

We are cleansed through Baptism to receive the Holy Spirit which connects us to the Church

Not that in the waters we obtain the Holy Spirit; but in the water, under (the witness of) the angel, we are cleansed, and prepared for the Holy Spirit. In this case also a type has preceded; for thus was John beforehand the Lord’s forerunner, “preparing His ways.” Thus, too, does the angel, the witness of baptism, “make the paths straight” for the Holy Spirit, who is about to come upon us, by the washing away of sins, which faith, sealed in (the name of) the Father, and the Son, and the Holy Spirit, obtains.

Moreover, after the pledging both of the attestation of faith and the promise of salvation under “three witnesses,” there is added, of necessity, mention of the Church; inasmuch as, wherever there are three, (that is, the Father, the Son, and the Holy Spirit, ) there is the Church, which is a body of three.

Tertullian
On Baptism
Chapter VI

Any kind of natural water is suitable for Baptism when the water is blessed

And accordingly it makes no difference whether a man be washed in a sea or a pool, a stream or a fount, a lake or a trough; nor is there any distinction between those whom John baptized in the Jordan and those whom Peter baptized in the Tiber, unless withal the eunuch whom Philip baptized in the midst of his journeys with chance water, derived (therefrom) more or less of salvation than others. All waters, therefore, in virtue of the pristine privilege of their origin, do, after invocation of God, attain the sacramental power of sanctification; for the Spirit immediately supervenes from the heavens, and rests over the waters, sanctifying them from Himself; and being thus sanctified, they imbibe at the same time the power of sanctifying.

Tertullian
On Baptism
Chapter IV

God gave life to all things through water and through Baptism gives new life

After the world had been hereupon set in order through its elements, when inhabitants were given it, “the waters” were the first to receive the precept “to bring forth living creatures.” Water was the first to produce that which had life, that it might be no wonder in baptism if waters know how to give life.

… it is not to be doubted that God has made the material substance which He has disposed throughout all His products and works, obey Him also in His own peculiar sacraments; that the material substance which governs terrestrial life acts as agent likewise in the celestial.

Tertullian
On Baptism
Chapter III

Baptism is such a simple act but obtains eternal life

There is absolutely nothing which makes men’s minds more obdurate than the simplicity of the divine works which are visible in the act, when compared with the grandeur which is promised thereto in the effect; so that from the very fact, that with so great simplicity, without pomp, without any considerable novelty of preparation, finally, without expense, a man is dipped in water, and amid the utterance of some few words, is sprinkled, and then rises again, not much (or not at all) the cleaner, the consequent attainment of eternity is esteemed the more incredible.

Tertullian
On Baptism
Chapter II

Christians are reborn through water Baptism

Happy is our sacrament of water, in that, by washing away the sins of our early blindness, we are set free and admitted into eternal life!

But we, little fishes, after the example of our ΙΧΘΥΣ Jesus Christ, are born in water, nor have we safety in any other way than by permanently abiding in water; so that most monstrous creature, who had no right to teach even sound doctrine, knew full well how to kill the little fishes, by taking them away from the water!

Tertullian
On Baptism
Chapter I

Confession is a second reserve against hell after Baptism

Therefore, since you know that after the first bulwarks of the Lord’s baptism there still remains for you, in exomologesis a second reserve of aid against hell, why do you desert your own salvation? Why are you tardy to approach what you know heals you?

Tertullian
On Repentance
Chapter XII

Christians are baptised by immersion into three persons

After His resurrection He promises in a pledge to His disciples that He will send them the promise of His Father; and lastly, He commands them to baptize into the Father and the Son and the Holy Ghost, not into a unipersonal God. And indeed it is not once only, but three times, that we are immersed into the Three Persons, at each several mention of Their names.

Tertullian
Against Praxeas
Chapter XXVI

The Father and the Son are distinct from each other because they speak to each other

On your side, however, you must make Him out to be a liar, and an impostor, and a tamperer with His word, if, when He was Himself a Son to Himself, He assigned the part of His Son to be played by another, when all the Scriptures attest the clear existence of, and distinction in (the Persons of) the Trinity, and indeed furnish us with our Rule of faith, that He who speaks, and He of whom He speaks, and to whom He speaks, cannot possibly seem to be One and the Same.

Still, in these few quotations the distinction of Persons in the Trinity is clearly set forth. For there is the Spirit Himself who speaks, and the Father to whom He speaks, and the Son of whom He speaks. In the same manner, the other passages also establish each one of several Persons in His special character—addressed as they in some cases are to the Father or to the Son respecting the Son, in other cases to the Son or to the Father concerning the Father, and again in other instances to the (Holy) Spirit.

Tertullian
Against Praxeas
Chapter XI

The body makes is possible for the soul to be saved through the sacraments of the Church

And since the soul is, in consequence of its salvation, chosen to the service of God, it is the flesh which actually renders it capable of such service. The flesh, indeed, is washed, in order that the soul may be cleansed; the flesh is anointed, that the soul may be consecrated; the flesh is signed (with the cross), that the soul too may be fortified; the flesh is shadowed with the imposition of hands, that the soul also maybe illuminated by the Spirit; the flesh feeds on the body and blood of Christ, that the soul likewise may fatten on its God. They cannot then be separated in their recompense, when they are united in their service. Those sacrifices, moreover, which are acceptable to God—I mean conflicts of the soul, fastings, and abstinences, and the humiliations which are annexed to such duty—it is the flesh which performs again and again to its own especial suffering.  Virginity, likewise, and widowhood, and the modest restraint in secret on the marriage-bed, and the one only adoption of it, are fragrant offerings to God paid out of the good services of the flesh.

Tertullian 
On the Resurrection of the Flesh
Chapter VIII