OP: You're not doing it wrong. The Warlock just fundamentally sells itself as something it's not (which is, lamentably, another example of 3e's DNA showing up in 5e). @
Sword of Spirit has the right of it--Warlocks simply aren't really casters in-combat. If you are expecting your contribution to combat to be spells, you're going to be disappointed by the Warlock. Ironically, another poster presented what I assume is
exactly your problem as though it were the selling point of the class:
How long are you finding combats to last? At 2 spells per short rest, 2 short rests per long rest, and 6-8 encounters per day you get almost 1 spell per encounter. <snip> Don't expect them to beat a wizard or sorcerer at their own game. Warlocks have much more sustained power but less options in their spell list and less ability to combo with it.
That is, with "almost" 1 spell per encounter, you pretty much flat-out
cannot be defined by actual "spell" casting (e.g. not counting cantrips as "spells"), because there will be 1-3 encounters a day where you aren't able to use any "spells" at all...and that's if you never cast a single out-of-combat spell. (Admittedly, Warlocks have some ways to get a few at-will utility spells, but they're very constrained in terms of what's available.)
The problem is that the Warlock is
sold as being "just another caster," in much the same way the Druid is sold as another caster. But the Druid very much still plays by the same rules as the Wizard does, while the Warlock is a very different beast. It comes close, though IMO not close enough, to being the "simple caster" option that WotC initially promised before dropping. You never have more than a handful of spells (reduced bookkeeping), and you have much of your power stored in passives, at-wills, or
basic attacks cantrips. Your spells are always of a specific power level. Etc.
Another way of putting this is that, although the Warlock eventually gets (some) access to spells of all levels, it should really be understood as closer to the Paladin, Ranger, and Eldritch Knight than it is to the Wizard, Sorcerer, or Druid. The Paladin in particular; Paladins
do have spells, but actually casting spells in combat (other than to get a useful buff in) is something you would expect Paladins to rarely do. The Warlock stands right on the cusp between being a "half-caster" like the first three, and a "full caster" like the second three. (sort of where the early playtest Sorcerer was; god I wish they hadn't dropped that...).
I strongly suspect that what your friend "truly" wants is a Wizard, or perhaps a Sorcerer if mixing it up in melee is important, who dallies with dark forces or pursues forbidden paths to power. The
fluff of the Warlock, but the
mechanics of the Wizard. The problem is, the Warlock is not only not a Wizard, it cannot
be a Wizard--it just doesn't have the tools. The 5e Warlock is a meleeist or "archer-with-spells," who can pull out a couple of powerful tricks now and then. She is not a master of all things arcane
on the battlefield. She is not playing magic chess, weighing the pros and cons of sacrifices now or difficult positions later. It's a lot more like...magical
checkers (draughts, for our UK siblings). It's on the same board, and has similar rules if you squint, but the strategy of it is very different and (generally speaking) vastly simplified.
So I guess I should amend my opening statement. You may in fact be doing the Warlock wrong: not because you're playing it wrong, but because the expectations it's held to cannot be met. To use a somewhat hyperbolic analogy, you've bought a Persian and you're profoundly disappointed that it doesn't play fetch, enjoy going on walks, bark, or lay its head on your lap and stare up at you with big soulful doggy eyes. (Though really in my experience Wizards are the ones more like cats...)