Ok, then. if channelling works, then good, but don't limit yourself to that...
Imagine this as a side view of where you're embarking...
_____
#####\
########\____________ ____ <- 'ground level'
#####################~~####
###########################
When viewing at 'ground level', the plan view you get will show you the surface. Here, I've also put a hill to the left, and a bit of water. (Although if you've embarked upon a perfectly flat plane, or on the top of a hill, this won't be something relevant to you.)
To get underground, you could dig sideways into the hill with your 'normal' mining operation as given by your normal (d)esignate(d)igging.
_____
#####\__
#####________________ ____ <-Dig sideways, note that the floor on the level above
#####################~~#### will stay up (at least until you disconnect it /all/,
########################### and then it'll cave in... read up on cave-ins!)
If (as you have done) you channel with (d)esignate-c(h)annel then you have access to the level below, from which you can (d)(d)ig sideways from the bottom of the ramp that you'll create on Z-1 (the term we here tend to use for 'the level below', according to context, Z+1 being the level above, etc).
_____
#####\
########\____ _______ ____
#############v#######~~#### <-Channel (creates a ramp)
###########################
_____
#####\
########\____ _______ ____
#############\___####~~#### <-Dig away from the lower ramp
###########################
If you dig away all edges, the ramp isn't viable (it just leaves a skylight)
#####\
########\____ _______ ____
##########_______####~~#### <-Now things down here aren't accessible from the ground, and vice-versa
###########################
But you can also (d)esignate stairwells to be dug. On the surface, you'll only be able to dig a downward-stairwell, and you'd also need to designate an upward-capable stairway (either an up-stair or a combined up/down-stair) on Z-1, directly below the down-stair. If you dug into the hillside, on Z=0, then you'd have an option of all three stairs (up, up/down and down) in any as-yet-undug tile, to which you'd need the appropriate stairs on Z+/-1 to match up. In a tile that is 'empty' (including with or without a 'floor', but either dug out or not filled in the first place), then (b)uilding and (c)onstructing an appropriate stairway is what you need.
_____
#####\__
########\_____>______ ____ <-Dig a downwards stairwell
#####################~~####
###########################
###########################
_____
#####\__
########\_____>______ ____ Match with an up/down stairwell,
###########___X___###~~#### <-and you can dig away sideways
########################### (in any and all directions)
###########################
#####\__
########\_____>______ ____ But don't dig into standing water,
###########___X_~~~~~~~#### <- unless you know what you're doing
########################### and wanting the resulting flood!
###########################
_____
#####\__ You don't need to make an up-only stairwell,
########\_____>______ ____ at the bottom, but it's all rather neat and tidy
###########___X___###~~#### if you /really/ don't intend to go further.
######________<_________### <- (and the water on the level above has a floor
########################### that I can't easily show, but you /will/ get
"this stone is damp"-type warnings.
In this case safe, but beware of aquifers!
_____
#####\__
########\_____>______ ____ And you can dig an upwards stairwell,
###########___X___###~~#>_# <-and match with a downward on the level above,
######________<_________<## but beware that you don't dig upwards into water
########################### (or magma, or possibly somewhere open
but populated by nasty fauna!)...
#####\__
########\_____X______ ____ Actually /Building/ an up-down stairwell on
###########___X___###~~#>_# <-your initial down-stairs lets you go upwards
######________<_________<##
###########################
#####\__ > <-But you'd need to Build a matching stair
########\_____X______ ____ on the level above, too...
###########___X___###~~#>_#
######________<_________<##
###########################
#####\__ ___>____ <-And now you can (b)uild and (c)onstruct
########\_____X______ ____ a (f)loor away from that.
###########___X___###~~#>_#
######________<_________<##
###########################
...but that's getting into advanced non-mining techniques. ;)