If a word has an affricate in the onset, let's say /ts/, along with another consonant, let's say /k/, to make a word like /tski/, is the phonotactic syllable structure of this word CCV or is it CCCV?
It depends on the language, and how you choose to analyze it.
In the phonetic sense, an affricate is a consonant cluster consisting of a stop that is released directly into a fricative, with no intervening release burst before the start of the fricative. Affricates may or may not be phonemic; that depends on whether the affricate behaves phonologically/phonotactically as an indivisible unit.
An example is the cluster [tˢs]. In Japanese, it patterns as a phonemic unit; in fact, it alternates with (compare [matsu] waits with [mata] waited), and is often considered an allophone of, the single phoneme /t/. In contrast, in English, [tˢs] is a sequence of 2 phonemes rather than a phoneme, because it patterns like the sequence /t/ + /s/ (in words like cats /kæts/ the /t/ and /s/ belong to different morphemes, so /ts/ is clearly not a unitary phoneme).
Another case is [tɕ] in Russian. This is clearly a phonemic affricate: because Russian doesn't even have a phoneme /ɕ/, it's not even possible to analyze it as a sequence.
Whether to consider a (phonetic) affricate as two separate consonants in the onset depends on whether you are considering it as a non-phonemic sequence. Phonotactic considerations can also guide you here.
Example: /tʃ/ in Spanish. There are 2 arguments that this should be considered a single consonant in the onset:
In your particular example, treating it as /CCV/ is more likely, since it's uncommon for languages to permit 3 obstruents in the onset, but /CCCV/ is also possible.