I am having trouble in my learning materials finding the basic construction for the idea of needing and wanting to do an action. In Spanish we use "I want" or "I need" plus the infinitive.
Example: Yo quiero "salir" con el. (I want "to leave" with him)
Yo quiero "aprender" "hablar" gaelico.
(I want "to learn" "to speak" Irish.). This uses two infinitives stacked.

Is there a similar construction in Irish that is a pattern that can be used?

I want to eat now.
I want to go there with him.
I need to learn some words.
I want "to go" there "to learn" this.

Slan,
Faber

yo quiero = "Ba mhaith liom" (I would like) or "Is mian liom" (I intend to)

I'll give you examples. Analysis is beyond me - I work on instinct!

The "I want" ones:
Ba mhaith liom labhairt na Gaeilge a fhoghlaim
Ba mhaith liom ithe anois
Ba mhaith liom dul ansin chun seo a fhoghlaim

"I need" is more fluid
You could use the verb caithim ("I must" is one of its many meanings)

Caithfidh mé roinnt focail a fhoghlaim.

But there are other ways to say need:
Tá leabhar nua de dhíth orm
or even more simply
Tá leabhar nua uaim

Hasta lluego.

Roinnt focal nó roinnt focla, chan *roinnt focail.

Is mian liom is not "I intend to" but "I want to".
I intend to = Tá sé ar intinn agam...

Tá débhrí ag baint le "want" sa Bhéarla - cíallíon sé idir gá agus fonn a bheith ort.

mian [ainmfhocal baininscneach den dara díochlaonadh]
dúil, fonn; ábhar na dúile sin (is tú mian mo chroí); (leis an gcopail) toil (más é is mian leat).

Toil a bhí i gceist agam nuair a dúirt mé "intend"

Tá dheá bhrí ag "want" i mBéarla, cgl.

Ach bhí an abairt i nGaeilg, agus níl an chiall "intend" ag "is mian le...", de réir fhoclóir Uí Dhónaill (lch. 854). Tá mé rófhalsa leis an pharagraf uilig a scríobh anseo, so amhanc thusa air :-) : "mian", 3ú paragraf "with copula".

Lughaidh, the last sentence in the dictionary entry you have quoted is:

Is é rud ba mhian liom a rá (go) what I meant to say was (that)

That can also be expressed as "what I intended to say was (that)", so your statement "níl an chiall 'intend' ag 'is mian le...'" is incorrect. Aonghus' explanation was fine. His point was that there is no directly equivalent verb, and he is right.