As with so many things, this breaks down into a nice linear process:
- Roll ability scores: strength, intelligence, wisdom, constitution, dexterity, charisma. I have to admit here that I still use this order of stats, which was the OD&D method. AD&D normally lists them with constitution and dexterity swapped.
- Pick your race. You may pick any race that your ability scores will qualify you for including the racial bonuses and penalties for that race. So, for example, a set of scores which include 11 constitution will allow a character to be a dwarf as the +1 constitution of that race will bump the score to the minimum required.
- Pick your class or (if non-human) classes, possibly restricted by race (PHB p14 and pp16-17).
- Pick your alignment, possibly restricted by class.
- Find the character's age (DMG p12).
- Adjust the character's ability scores to reflect their age (DMG p13). You can't now go back and pick a different class!
- Roll hit points! Now your character can fight!
- Roll up secondary skills (DMG, p12) if applicable.
- Roll up starting cash. Multi-class use the best row of the table on PHB p35.
- Spend it.
- Spell-casters (clerics, druids, magic-users, illusionists) pick their spells (magic users and illusionists use the rules on DMG p39).
Firstly, #1 - roll ability scores. The DMG presents four methods (I-IV). Back in ye olden days, method I was probably the most popular. It's quick and reasonably good at generating decent score sets.
Nowadays, however, with computers and laptops and smartphones and all those sorts of things, the other systems can be utilized with no real time penalty. Given this, I prefer now to use Method IV.
Secondly, the Players Handbook has a note to the effect that characters should have two scores of 15+. I don't entirely agree with this, but again it can be factored into a computer program so that it only offers scores which fit this criterion. In fact, I have done such a thing and you can access it here, at least when my dreadful Internet connection is working (avoid TalkTalk, folks). Ironically, I think this suggestion is of less use to beginners than to experienced players who know what to do with higher stats. Anyway, it's up to the DM to decide.
Thirdly, there's a misprint in some early editions of the PHB which put the half-orc's maximum dexterity at 14. It should be 17. There's a full PHB errata list over at the Acaeum website, as well as one for the DMG, the MM and the notoriously extensive one for Unearth Arcana, should you decide to use UA in your games.
Alignment next time, I think.