How do you avoid it with lead solder? Common soldering tutorials don't mention the issue.

Because lead poisoning isn't a huge issue for hobbyists.

Common rules are: Work in a well-ventilated area, don't eat while working, don't use your soldering iron to heat your coffee. But those apply while using lead-free solder as well.

Why is it not an issues, the dosage is too low? Afaik lead enters through the skin, too - washing hands after soldering sufficient?

Real answer: you would have to be soldering for hours every day for months to be exposed to more lead than can be cleared naturally. Full-time component assembly workers do get that much exposure, so they need to take precautions to avoid poisoning. For hobbyists, you would have to eat quite a bit of solder at once before you would develop any poisoning symptoms.

edit: so, it's the frequent repeated exposure to lead (i.e. in paint and as a sugar added to wine[0]) which is harmful, not any single individual (non-acute) exposure.

[0]: https://en.wikipedia.org/wiki/Lead(II)_acetate#Sweetener

heavy metal leaching in rubbish tips is an environmental issue, one being tackled by much of Europe, starting with regulations on lead-containing electronics.

And since almost all electronics are made in large quantities for sale, it makes sense that there can be different rules for one-offs.

Don't eat the solder? Warning: Pregnant women, the elderly, and children under 10 should avoid prolonged exposure to lead-based solder. Caution: lead-based solder may suddenly accelerate to dangerous speeds. Lead-based solder contains a liquid core, which, if exposed due to rupture, should not be touched, inhaled, or looked at. Do not use lead-based solder on concrete. Discontinue use of lead-based solder if any of the following occurs:

    itching
    vertigo
    dizziness
    tingling in extremities
    loss of balance or coordination
    slurred speech
    temporary blindness
    profuse sweating
    or heart palpitations. 

If lead-based solder begins to smoke, get away immediately. Seek shelter and cover head. Lead-based solder may stick to certain types of skin. When not in use, lead-based solder should be returned to its special container and kept under refrigeration. Failure to do so relieves the makers of lead-based solder, Wacky Products Incorporated, and its parent company, Global Chemical Unlimited, of any and all liability. Ingredients of lead-based solder include an unknown glowing green substance which fell to Earth, presumably from outer space. Lead-based solder has been shipped to our troops in Saudi Arabia and is being dropped by our warplanes on Iraq. Do not taunt lead-based solder. Lead-based solder comes with a lifetime warranty.