How to start playing…

1. …the mandolin
2. …the mandola
- 2.1. Getting an instrument

1. …the mandolin

1.1. Getting an instrument

1.1.1. Just to try it out

Check out local libraries! Teaching students how to play I was surprised to find that our library lends out (cheap but acceptable) mandolins. For free!
Check out auctioning websites! Vintage instruments sometimes even go for single-digit prices, as the mandolin used to be very popular. But few people know what the weird, small guitar grandpa had tucked away is.

With a proper setup and restringing by a luthier (for example the Saitenschiff; or, if you're a bit crafty, yourself), often these instruments turn out to be surprisingly playable! With a bit of luck, you can get a very good instrument for less than a hundred Euros.

1.1.2. Buying

Once you're certain about wanting to learn, don't cheap out too much. Sub-100€-instruments exist, and I've held some which sound and play nice. But similar to auctioning it can be a bit of a gamble. You will have to spend a three-digit sum to get an instrument you'll be happy with for more than a few years.
On the other hand: Don't spend too much and focus on the essentials.
- An acoustic without pickup is preferable to one with a pickup at the same pricepoint. Whatever money goes into the electronics likely reduces the care and materials going into the acoustic properties. Also, most pickups impair the plain acoustic sound in some way.
- Don't forget to budget for the accessoires which you might want.
  - A strap is essential in my opinion.
  - Some sort of mandolin school can make things way easier. It gives you something to work through.
  - At least one spare set of strings. Strings are easy to change on most modern mandolins.
  - If you want to play with others: A case or bag
  - A metronome / tuner / combination thereof can likely be forgone in the age of smartphones. They're still nice to have, though.
A few personal opinions:
- American "Bluegrass" mandolins are preferable. They're easier to hold and play, restringing is easier, I prefer the sound, and at a similar pricepoint a flat mandolin will tend to have a higher general playability (as quite a bit of money for a bowlback goes into build the bowl).
- Setup and restringing is easy! At least for flatbacks. Have someone show it to you once, and then do it on your own.
- Even the cheapest mandolin strings are fine to play on. Actually, some people might actually prefer their tone.
- I've never held a 1k+€ instrument in my hands, but I doubt most people will even reach the point where they notice the difference to a 500€ instrument in fewer than five years (if at all). Don't overspend at the beginning.

1.2. Learning to play

1.2.1. Main tips

Play daily! I don't care how long, I don't care when, I don't care what. If you want to improve at any skill, you will have to practice it daily.
On a related note: Pick at least one song you want to be able to play early on.
On the other hand: Don't play for hours on end at the beginning! Your fingers will need to build up callouses and there's also a bit of muscle building involved at the beginning.
Vary what you're practicing. I know you will feel like you're making more progress if you're playing the same pieces every day, but there's a danger of limiting oneself too much.
Playing with others (such as an amateur orchestra) is more fun and motivating.

1.2.2. How to go about it

First steps
1. Practice downstrokes on (all) open strings. Let your pick rest on the next string at the beginning. These "rest strokes" give a particularly full sound and are easier to do at the beginning.
2. Play frets 0,2,4,5,(7) on one string in turn. Those are the first four (five) tones of the major scale starting on the strings' base tone. Skip the seventh (and possibly the fifth) fret until you feel comfortable with the rest. Fret like this:
  
  Fret Finger
  
  0 /
  
  2 First
  
  4 Second
  
  5 Third
  
  (7) Fourth
3. You now can play the following scales by repeating the pattern across two adjacent strings:
  
  Scale Strings
  
  G major G,D
  
  D major D,A
  
  A major A,E
  
  Each scale ends on fret 5 of the higher string. All notes for the G major scale:
  
  fret / string G D
  
  0 g, d
  
  1
  
  2 a, e
  
  3
  
  4 b, fis
  
  5 c g
  
  6
  
  7 d (a)
  
  As soon as possible, play at least one scale a day up and down.
4. The next pattern is:
  
  Fret Finger
  
  0 /
  
  2 First
  
  3 Second
  
  5 Third
  
  (7) Fourth
  
  Those are the first four (five) tones of the minor scale starting on the strings' base tone. Skip the seventh (and possibly the fifth) fret until you feel comfortable with the rest.
  
  You can now play the G major scale over all four strings, ending on fret 3 of the e' string:
  
  fret / string G D A E
  
  0 g, d a e'
  
  1
  
  2 a, e b fis'
  
  3 c' g'
  
  4 b, fis
  
  5 c g d' (a')
  
  6
  
  7 d a e' (b')
  
  You can of course also extend the D major scale up to the e' string.
5. Finally, add this pattern:
  
  Fret Finger
  
  0 /
  
  1 First
  
  3 Second
  
  5 Third
  
  (7) Fourth
  
  This fits on top of pattern two to:
  1. Build e.g. the A minor scale:
    
    fret / string A E
    
    0 a e'
    
    1 f'
    
    2 b
    
    3 c' g'
    
    4
    
    5 d' a'
    
    6
    
    7 e' (b')
  2. play e.g. the F major scale:
    
    fret / string D A E
    
    0 (d) a e'
    
    1 bes f'
    
    2 (e)
    
    3 f c' (g')
    
    4
    
    5 g d' (a')
    
    6 (bes')
    
    7 a e'
6. As soon as possible, include the fourth ("pinky") finger in your playing.

Fret	Finger
0	/
2	First
4	Second
5	Third
(7)	Fourth

Scale	Strings
G major	G,D
D major	D,A
A major	A,E

fret / string	G	D
0	g,	d
1
2	a,	e
3
4	b,	fis
5	c	g
6
7	d	(a)

Fret	Finger
0	/
2	First
3	Second
5	Third
(7)	Fourth

fret / string	G	D	A	E
0	g,	d	a	e'
1
2	a,	e	b	fis'
3			c'	g'
4	b,	fis
5	c	g	d'	(a')
6
7	d	a	e'	(b')

Fret	Finger
0	/
1	First
3	Second
5	Third
(7)	Fourth

fret / string	A	E
0	a	e'
1		f'
2	b
3	c'	g'
4
5	d'	a'
6
7	e'	(b')

fret / string	D	A	E
0	(d)	a	e'
1		bes	f'
2	(e)
3	f	c'	(g')
4
5	g	d'	(a')
6			(bes')
7	a	e'

1.3. More resources

Mandolincafe: A huge repository of links, knowledge, and music.
Mandoisland: A lovingly handcrafted webpage about all things mandolin. Lots of free sheet music!
Solo-Mandolin Pieces on IMSLP: Free (mostly classical) sheet music. You can also check out pieces arranged for mandolin. And there's also music featuring the mandolin.

2. …the mandola

For most information, the tab "…the mandolin" also applies here.

2.1. Getting an instrument

Slightly more difficult. You will probably have to buy a used instrument to get away cheaply, and trying it out beforehand might be difficult. Do check out luthiers (In the southwest of Berlin I can recommend the Saitenschiff).

You can also ask us from the MVB to test-play a mandola before looking to buy one.