Analyzing text according to Michael Halliday's functional grammar framework for transitivity analysis requires understanding the key concepts behind Halliday's framework of functional transitivity. In essence, Halliday's transitivity analysis uses a function-focused grammar to isolate functions and participants represented in clauses to determine the joint ideologies of social actuality combined with linguistic semantics, or socio-semantics, to understand the process(es) participants (who/what and whom/what) are engaged in or related through and in what circumstance(s) the process(es) of engagement/relationship occurs. In other words, transitivity analysis examines:

who (or what) did what to whom (or what) where, when, how and why.

Let's clarify by using a popular board game. Colonel Mustard murdered Mr. Boddy in the conservatory last night with the candlestick for the reason of revenge: who (Mustard) did what (murder) to whom (Boddy) where (conservatory) when (last night) how (candlestick) why (revenge).

In Halliday's functional grammar, murder is the verb phrase (VP) process of the clause; the participants are Mustard and Boddy; the circumstances are where, when, how and why. [This model may also be expressed as somebody (or something) did something to someone (or something) somewhere, some time, with something and for some reason.] Another example using the what/what alternatives is: The tree (what) broke (did what) the car (what) in the car park an hour ago because of the fierce wind for no reason whatsoever. Of course combinations are possible too: The tree scared the boy ...; the boy cut the tree ....

Halliday's transitivity analysis reveals the social dynamic between the Subject Actor and the Object Goal while at the same time revealing the linguistic structure that supports and represents the social process (verb phrase). In his framework, the ideologies of linguists and sociology meet and expand upon each other through the ideation each functional element carries. Additionally, the ideology of authorial expression meets the ideology of reader/listener comprehension backed by similar or different experience and knowledge. In these manners, Halliday's transitivity (the transfer of action/process/verb from Actor to Goal or the absence of transfer of action) is said to combine ideologies through ideation.

Now to apply this to your website example above.

Process/Verb Phrase (P)
Actor (A)
Goal (G)
Subject (S)
Object of Verb (O)
Complement of Subject (C)
Adjunct (where, when, how, why) (Ad)

"[I]f we were going to have a wet day, we might as well see the Ingleton Falls at their most dramatic."

[I]f we (Actor Subject/who) were going to have (Process/ Verb Phrase Predicator) a wet day (Goal Complement/what), we (A) might as well see (P/VP) the Ingleton Falls (G/O) at their most dramatic (Adjunct).

In both clauses, the verb phrase social process has transitivity because the Actor and the Complement or Object--the Goal--transfer the effect of the process between themselves: the A/G are not unaffected by the other.

[It seemed {that we (A/S) had got (P) that bit right (when we spoke to the bloke at the car park) (O)}]

This is more complicated because of two embedded clauses and a delayed Subject with a "dummy it." Space dwindles, but I'll do the embedded when-clause and dummy it clause.

(when we (A) spoke to (P) the bloke (O) at the car park (Ad))

[It (A/S) seemed (P) {that we had got that bit right when we spoke to the bloke at the car park} (C)]