The gerund is a verbal noun. To form the gerund, add -nd- to the present stem of the verb:

portand-

docend-

trahend-

capiend-

audiend-

plus the neuter endings of the second declension:

Genitive	portandī
Dative	portandō
Accusative	portandum
Ablative	portandō

The gerund is always singular, and the nominative is supplied by the infinitive.

The gerundive is a verbal adjective, sometimes called the future passive participle; it is the same form that, combined with forms of the verb sum, esse, fuī, forms the future passive periphrastic. Its stem is the same as the stem of the gerund, and it declines like any other first/second declension participle (like bonus, -a, -um):

portandus, -a, -um

docendus, -a, -um

trahendus, -a, -um

capiendus, -a, -um

audiendus, -a, -um

Use of the gerund and gerundive:

The gerund functions like any other noun, but (because it is a verbal noun) it can take an object, be modified by an adverb, etc. If a verb governs the dative case, so will its gerund.

Pōlla postēs iānuae unguendō fascinātiōnem āvertit.

Pōlla averts the evil eye by anointing the posts of the door.

Here, unguendō is the ablative of the gerund; it's an ablative of means; postēs is its direct object.

Helvidius hortum ingressus est ad Pōllam videndum.

Helvidius entered the garden to see Polla.

Here, videndum is the accusative of the gerund; it's an accusative object of the preposition ad, used to express purpose; Pōllam is its direct object.

Helvidius domum Sparsī appropinquat eum interficiendī causā.

Helvidius approaches the house of Sparsus for the sake of killing him.

Here, interficiendī is the genitive of the gerund; it's genitive with causā. eum is its direct object.

But (and here's the tricky part) when a gerund would take an accusative direct object (as in all the examples above), a gerundive construction is preferred:

Pōlla postēs iānuae unguendō fascinātiōnem āvertit.

becomes

Pōlla postibus iānuae unguendīs fascinātiōnem āvertit.

Pōlla averts the evil eye by anointing the posts of the door.

Now, postibus is the ablative of means, and unguendīs is the masculine ablative plural of the gerundive agreeing with it.

Helvidius hortum ingressus est ad Pōllam videndum.

becomes

Helvidius hortum ingressus est ad Pōllam videndam.

Helvidius entered the garden to see Polla.

Now, Pōllam is the accusative object of the preposition ad, used to express purpose, and videndam is the feminine accusative singular of the gerundive agreeing with it.

Helvidius domum Sparsī appropinquat eum interficiendī causā.

Helvidius domum Sparsī appropinquat eius interficiendī causā.

Helvidius approaches the house of Sparsus for the sake of killing him.

Now, eius is the genitive with causā, and interficiendī is the masculine genitive singular of the gerundive agreeing with it.