First things first - make a budget
Figure out how much money you earn, what you spend it on, and how that will change when you have kids (will one of you stay at home? if not, how much will daycare cost and how do you finance the first few month when your child is still too young for daycare?)
You will usually plan to spend your current Kaltmiete (rent without utilities) on your mortgage (the Darlehen that is secured by your house) - keep in mind though that a house usually has a higher utility cost than an appartment.
When you've figured out what you can save/pay towards a house now and how that will change when you have kids, you can go on to the next step.
Option A) Buy later but with today's low interest rates
If you don't want to buy now but want to commit to saving up for a house and also want to secure today's really low interest rates, consider getting a "Bausparvertrag".
I didn't find a good translation for Bausparvertrag, so here is a short example of how it works: You take a building saving sum (Bausparsumme) of 150000€ with a savings goal (Sparziel) of 50000€ (the savings goal is usually between 20% and 50% of the sum) and then you make monthly payments into the Bausparvertrag until you reach the savings goal at which point you can take out your savings and a loan of 100000 € (or whatever your difference between the Bausparsumme and Sparziel is). If you're living in an expenisve area, you're likely to need more than 150000 but this is just an example.
- you agree on the interest of the loan today - you'll likely get 1.5% or lower - so you don't have to worry about rising interest rates in the future.
- you get approved for the loan today so you don't have to worry about getting approved later.
- you get very little interest on your savings during the savings phase.
- you pay a one time fee of 1%
- you can only take the loan if you use it to buy a house/appartment or to refinance one.
If you decide to buy sooner, you can also use your Bausparvertrag to refinance later.
Option B) Buy today
If you have a decent income and a permanent job, then ask your bank if they would consider financing your house now. To get a sense of what you'll be able to afford, google "wie viel Haus kann ich mir leisten" and use a few of the many online calculators. Remember that these websites want to sell you on the idea of buying a house instead of paying rent, so they'll usually overestimate the raise in rents - repeat the calculation with rent raise set to 0% to get a feeling for how much you'll be able to afford in today's money.
Also, don't forget that you're planning to get children, so do the calculation with only one income, not two, and add the cost of raising the kids to your calculation.
Once you've decided on a property, shop around a bit at different banks to get the best financing.
If you decide to buy now (or soon), start looking at houses now - go to model homes (Musterhäuser) to find out what style of house you like - this is useful whether you want to buy an existing house or build a new one. If buying an existing house is an option for you, start visiting houses that are on sale in your area in order to practice what to ask and what to look for. You should have a couple of visits under your belt before you really start looking for the one you want to buy.
Once you're getting closer to buying or making a contract with a construction company, consider getting an expert "Bausachverständiger". When buying an existing house they can help you estimate the price and also estimate the renovation cost you'll have to factor in for a certain house (new heating, better insulation, ...). When building a new house they can advise you on the contract with the construction company and also examine the construction company's work at each major step (Zwischenabnahme).
Source: Own experience.