Long means to have bought, to be an owner of an asset, in the hope its value will rise, allowing me to sell at a higher price later.
Short means the opposite, to have taken a position which will run into profit if the value falls. e.g. I recently placed a spreadbet that the value of the Euro would fall compared with the $. The further the ratio fell, the more profit was made as this was a spreadbet, i.e. a bet not just on direction, up or down, but also on the distance , downwards in this case.
Uptrend is a progression of rising prices over a timeframe (personally defined). There are various objective definitions drawn from what you see on a price chart, none of them is exclusive, but a useful pattern to seek out is a succession of higher highs and higher lows (price does not move upwards in a straight line like a 45 degree slope up the chart towards top right, it takes say 3 steps up, then 2 down then 3 up then 2 down etc. Each high should be higher than the last high, each low higher than the last low.
Reverse this for a downtrend.
In any case, bear in mind what is an uptrending share to you and me over the last 26 weeks might be a downtrending share to a daytrader over the last 26 hours.