Throws in

Preston North End take a throw in against Nottingham Forest.

 Let's take a look at the Football Association's 1863 law regarding the throw in:
  When the ball is in touch, the first player who touches it shall throw it from the point on the boundary line where it left the ground in a direction at right angles with the boundary line, and the ball shall not be in play until it has touched the ground.

Okay- so as in other cases of the ball going out of bounds there was still the matter of the return to be resolved by means of a touchdown. What follows has some similarities with the Rugby throw in- it must be at right angles with the touchline- so there was no territorial advantage to be gained from the throw itself. Also note that the ball had to touch the ground before it was back in play- so heading the ball  on (not that heading was a common practice in those days) or even volleying it forward from a throw was forbidden.
The manner in which the ball was thrown was not prescribed.
The Sheffield rules were similar in their description of what should happen when the ball crossed the sideline, whereas the Cambridge Rules required a kick-in. Bear in mind that the pitch could be up to 100 yards wide.

In 1866 the clause was added whereby the player throwing in could not play the ball again until it had been played by another player- so, as now, you couldn't take a throw in to yourself.

In 1868 the Sheffield Association introduced the kick in, but with the modernizing notion that it was awarded against the team who played the ball into touch. The opposition had to stay 6 yards away from the kicker (as it was, in effect, a free kick).
The FA retained the first to touch it down aspect of the rule, but in 1870 added the proviso that the ball had to travel at least 6 yards from the boundary line and touch the ground before it was in play.
The award of the throw in against the team who played the ball into touch was introduced by the FA in 1873 following a proposal from Nottingham Forest.

In 1877 the vital 'in any direction the thrower might choose' was added by the FA. Rather ambiguously the ball still had to travel 6 yards but was now in play once it was thrown- so it didn't have to touch the ground.
In Scotland the throw in rule remained unchanged - the throw still had to be taken at right angles.

In December 1882 a conference of the Football Associations of England, Ireland , Scotland and Wales was held in Manchester. The purpose of the conference was to standardise the rules. The throw in rule underwent an amendment which stipulated that the thrower must hold the ball above his head. A Manchester Guardian report at the time refers to this as 'virtually adopting the Scotch rule'. This was not the case, however, as in Scotland the practise of throwing in at right angles had been retained. In fact at an FA meeting in February1878 the representatives of Queen's Park had advocated for the right angle rule to be reimposed, and a proposal by Alexandria Athletic at the AGM of the Scottish FA in September, 1878 that the throw in should be allowed in any direction, met witth strong opposition and was not carried. 

In May 1880 the Scottish FA undertook a revision of their rules, but still they retained the right angle throw in. 
There was a need , however, to find some compromise in  international matches. The Football Association were most keen that 'their' rules should govern all matches, but the Scots were vehemently opposed to the notion of the throw in being taken in any direction, and had in fact experienced the (dis)advantageousness of this rule when they had played the English in 1879. The Scots had stuck to their right angle throw ins whilst the English had bowled mammoth throws into the goalmouth. The compromise was that the throw-in could be in any direction, but that the thrower must use both hands and throw from above his head. The Scots agreed to grant this method a one- year trial (they never went back to the right angle throw). 
In an FA committee  meeting  in January 1883, William Pierce-Dix of the Sheffield FA proposed that the two hands and thrown above the head method should become mandatory. This effectively gave us the Law governing the throw in as we now know it today.

see: The Football Association 1863-1883: A Source Book by Tony Brown (2011)