I've begun working on conlangs for some time and I generally like to start by going to the roots of the language, the really archaic forms, to figure out how it evolved early on. Normally I go about making a list of roots and seeing how those evolve into actual vocabulary, grammatical endings, etc. I'm just curious what other ways people go about the early development of their conlangs.
What I usually do is start with the "present-day" forms (for whatever value of present day) and then see where I can introduce cool diachronically motivated stuff. Usually that means making up some stuff, coming up with a "reconstruction" that could explain it, change stuff to fit these proto-forms, then decide I want the modern language to be different and changing the proto-forms accordingly, and so on. I'm not sure I have a really good example of this anywhere — I'm pretty terrible at publishing my stuff — but most of my conlangs change wildly until their prehistory is mostly clear, and then they kind of settle down.
I think if you zealously stick to growing a conlang from roots, the result will invariably be an unwieldy kitchen sink of diachronics with no cohesion, simply because you can't really emulate the nuances, connotations, and settling that would manifest in a real population of speakers over a long period of time. So, supplement with some kind of vision. Sindarin and Quenya come to mind—they do have big sections of vocabulary that Tolkien built forward, from roots, but these were practicable because he had a strong, academic familiarity with natlangs from the families he was trying to emulate, so navigating the waters of consistency wasn't really an issue.
To go even further: in statistics, there's an algorithmic paradigm called expectation–maximization. The idea is that you alternate between calculating two sets of variables meant to reflect each other, typically by determining the expected assignments of data points to randomly-generated distributions, then determining the best estimate distribution (by maximizing model parameters) that would have produced those assignments. Substitute these estimates for the randomly-generated ones, and you can repeat the process indefinitely. For a wide range of useful models, the numbers will eventually converge to an optimum. Sort of like when you feed text into Google Translate repeatedly and it eventually finds a pair of phrases (or a small group) that it loops between. You can (and should) do this with conlanging, too, by re-deriving your original roots from the final dictionary to ensure they're consistent. It probably won't require multiple iterations, though.
To go even further: in statistics, there's an algorithmic paradigm called expectation–maximization. The idea is that you alternate between calculating two sets of variables meant to reflect each other, typically by determining the expected assignments of data points to randomly-generated distributions, then determining the best estimate distribution (by maximizing model parameters) that would have produced those assignments. Substitute these estimates for the randomly-generated ones, and you can repeat the process indefinitely. For a wide range of useful models, the numbers will eventually converge to an optimum. Sort of like when you feed text into Google Translate repeatedly and it eventually finds a pair of phrases (or a small group) that it loops between. You can (and should) do this with conlanging, too, by re-deriving your original roots from the final dictionary to ensure they're consistent. It probably won't require multiple iterations, though.
If what you want is to figure out how archaic words or roots evolve into vocabulary that's fine, this is a thing most people do to some extent. But you ask for the ways we take when developing our conlangs in the early stages and, well, in my case it really depends on what I want to do with the language in question. Most of my conlangs are artlangs, and the main purpose concerning vocabulary is to create words with a certain, specific aesthetics that make up the language's flavour, or soul if you prefer.
I use to start with an idea for the language's flavour (how I want it to sound and to look), and then I create some words; sometimes the process is the opposite, since from some words that have a common flavour I may derive a language (or the primitive form of what will become a language). At some point I may create some basic roots and figure out how they evolved. This step may take weeks or months, and it's always a bidirectional process, like a conversation between the small, growing vocabulary, and the set of roots and protowords. It's a calibration process, like tuning a musical instrument, until I reach the flavour I want. After that step the vocabulary and the list of proto-roots have both increased notably.
In that tuning there's always discordant notes. Words that don't fit at all, not-so-suitable roots, word endings that looked good in the beginning but don't work at all now, misalignments with the phonology... It's part of the process, but instead of throwing these notes to the litterbin I make use of them when it's possible. They're a gift because with them I can work loanwords or rare words with obscure origins and substratum, adstratum, superstratum words. This makes sense to me because all my conlangs belong to a conworld, and there's contact between them.
I've used word generators as well, but I find them to be quite boring after playing a little with them. Some results, though, can be really good. A thing I like to do when starting a new vocabulary or set of proto-roots is to take a not very long list of words from whatever origin and rework the words and their meanings to fit my purposes. I derived the first roots of Bernic (one of my protolanguages) from a short list of Polari words (this one as well) I found in internet. So, for example, from medzer "half" I created mitsi "small", and from palone "woman", PALON– "female", and so on. Other Bernic words and roots, though, have been created from zero (for some reason I feel that kērtetso is a good Bernic word for "elm tree").
Edit: oh, I forgot to say that I find grammatical endings very important to work the desired language flavour. How endings look and sound are as important to me as how the words' cores and roots are worked. Not to mention how you choose to present the language's romanization, which is also very important aesthetically, in my opinion.
I use to start with an idea for the language's flavour (how I want it to sound and to look), and then I create some words; sometimes the process is the opposite, since from some words that have a common flavour I may derive a language (or the primitive form of what will become a language). At some point I may create some basic roots and figure out how they evolved. This step may take weeks or months, and it's always a bidirectional process, like a conversation between the small, growing vocabulary, and the set of roots and protowords. It's a calibration process, like tuning a musical instrument, until I reach the flavour I want. After that step the vocabulary and the list of proto-roots have both increased notably.
In that tuning there's always discordant notes. Words that don't fit at all, not-so-suitable roots, word endings that looked good in the beginning but don't work at all now, misalignments with the phonology... It's part of the process, but instead of throwing these notes to the litterbin I make use of them when it's possible. They're a gift because with them I can work loanwords or rare words with obscure origins and substratum, adstratum, superstratum words. This makes sense to me because all my conlangs belong to a conworld, and there's contact between them.
I've used word generators as well, but I find them to be quite boring after playing a little with them. Some results, though, can be really good. A thing I like to do when starting a new vocabulary or set of proto-roots is to take a not very long list of words from whatever origin and rework the words and their meanings to fit my purposes. I derived the first roots of Bernic (one of my protolanguages) from a short list of Polari words (this one as well) I found in internet. So, for example, from medzer "half" I created mitsi "small", and from palone "woman", PALON– "female", and so on. Other Bernic words and roots, though, have been created from zero (for some reason I feel that kērtetso is a good Bernic word for "elm tree").
Edit: oh, I forgot to say that I find grammatical endings very important to work the desired language flavour. How endings look and sound are as important to me as how the words' cores and roots are worked. Not to mention how you choose to present the language's romanization, which is also very important aesthetically, in my opinion.