You only conjugate one verb (the action verb) to the subject per sentence clause. The action verb here is 'necesitar' (to need). The subject is 'I' so that verb becomes 'necesito'. Anything that comes after that is what you need and not what you are doing. The verb 'beber' means 'to drink' and again, because you are not actually drinking something here you do not need to conjugate it.
Let me put it a different way: The important thing to note is that only one verb needs to match the subject. Any other verbs listed would be left in their natural unaltered state. So always ask yourself "What action is being performed here?" That will tell you which verb needs to match the subject.
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Think of your English sentence structure & apply it to Spanish. Where is your verb? Need. Who or what needs? I need. I need what? Water. What do you need water FOR? "To drink."
Spanish works the same mostly. So you would lay the sentence out the same. Verb need, nesecito. Who or what needs? I need. Yo necesito. What do you need? Water, agua. To drink FOR? para beber. Yo necesito agua para beber. Add in any other words as needed like Please, por favor. And you get: "Por favor, yo necesito agua para beber."
Hope this helps because it wasn't until I started doing this that I understood English & it wasn't until I started applying this in Spanish that sentence structure made sense. Like saying "I dont want." Or "I dont need." Do not want - the NOT is always before the verb. "Want" yet it seemed wierd where you put "Yo no quiero" sometimes to me, but once i thought about it, it SHOULD always be before thr verb - just like English! Even if its backwards in the Spanish sentence! Just remember your rules!
Except that in English “not” come after the conjugated part of the verb, “I do not...” and “he does not”. Most of the time, it would be better to learn Spanish word order for Spanish and English word order for English.
Watch out, you accidentally flipped your consonants on your first instance of “necesito”.