What is the correct way to use "would" and "should"?

Question

I have used these two words for ages that I sometimes forget that these words are past form of "will" and "shall". For example, I prefer:

I would like to introduce two members to our group.

Rather than:

I will like to introduce two members to our group.

Or even:

I like to introduce two members to our group.

Which sometimes I suspect it has the silent 'd word hidden somewhere that is shortened form of would.

I'd like to introduce two members to our group.

From my logic perspective, I still haven't introduce those two members, so if I really want to use the word, I must use "will", and not "would", as it happens in the near future. Or just omit the word and use "I like". But to use "would" in the sentence feels so right. I don't know why, maybe because I feel I have read this so often. Can anybody help to point out what's the correct practice to use would and should in this case and in general case. Thanks.

Answer 1

The first and the last sentence are correct (since I'd is a contraction of I would, in this context). 'Would' is also an indicator of intent, that you want to do something.

"I like to introduce..." is incorrect, unless you're saying you enjoy introducing two people in general.

I have never heard anyone use 'I will like to', unless it is a part of their regional dialect.